In - GSI · Poland Abstract The pro duction cross sections and the kinematical prop erties of primary residual n uclei ha v e b een studied in the reaction 208 Pb (1 A GeV) + d. Isotopic

Primary-residue production cross sections and

kinetic energies in 1 A GeV 208Pb on deuteron

reactions

T. Enqvist a;e;1, P. Armbruster a, J. Benlliure a;f, M. Bernas b,

A. Boudard c, S. Czajkowski d, R. Legrain c, S. Leray c,

B. Mustapha b;2, M. Praviko� d, F. Rejmund a;b,

K.-H. Schmidt a, C. St�ephan b, J. Taieb a;b, L. Tassan-Got b,

F. Viv�es a, C. Volant c, W. Wlaz lo c;g

aGSI, Planckstra�e 1, D-64291 Darmstadt, Germany

bIPN Orsay, IN2P3, F-91406 Orsay, FrancecDAPNIA/SPhN CEA/Saclay, F-91191 Gif sur Yvette, France

dCENBG, IN2P3, F-33175 Gradignan, FranceeDepartment of Physics, University of Jyv�askyl�a, P.O. Box 35, FIN-40351

Jyv�askyl�a, FinlandfUniversidad de Santiago de Compostela, E-15706 Santiago de Compostela, Spain

gJagellonian University, Institute of Physics, ul. Reymonta 4, 30-059 Krak�ow,Poland

Abstract

The production cross sections and the kinematical properties of primary residualnuclei have been studied in the reaction 208Pb (1 A GeV) + d. Isotopic distributionswere measured for all elements from titanium (Z=22) to lead (Z=82). The measuredkinematical properties of the residues were also used to disentangle the relevantreaction mechanisms, spallation-evaporation and spallation-�ssion. The fragmentseparator FRS at GSI, Darmstadt, was used to separate and identify the reactionproducts. The measured quantities are important for the design and planning of fu-ture radioactive-beam facilities and accelerator-driven systems. The measured dataof the present work are comprehensively compared with the experimental data fromthe reaction 208Pb (1 A GeV) + p.

Key words: NUCLEAR REACTIONS; d(208Pb,X), E = 1 A GeV; measuredprimary spallation cross sections of 573 isotopes from cesium to lead; measuredprimary �ssion cross sections of 272 isotopes from titanium to rhodium; measuredrecoil velocities; in- ight identi�cation in Z and A by magnetic spectrometer, ToFand energy-loss measurements; inverse-kinematics method; relevance for the

Preprint submitted to Nucl. Phys. A 7 November 2001

production of radioactive beams and the design of accelerator-driven subcriticalreactorsPACS: 24.75.+i, 25.40.Sc, 25.70.Mn, 25.85.Ge, 25.85.-w, 28.41.Kw

1 Introduction

In the series of our previous publications, nuclide production cross sections ofprimary residues and their kinetic-energy distributions from spallation reac-tions of high-energy protons (0.8 or 1.0 GeV) with heavy nuclei of gold, leadand uranium have been reported [1{5]. In the present paper, measured iso-topic yields and kinetic energies of primary residues in the inverse-kinematicreaction 1 A GeV 208Pb on deuteron will be presented.

The recent intense research in the �eld of spallation reactions has risen fromtheir importance in many technical applications. In the next-generation radio-active-beam facilities, the projectile fragmentation at relativistic energies hasbeen proposed as one of the major production methods [6]. The inverse-kinematics experiments provide reliable information on the reaction mech-anism and on the production cross sections of individual isotopes in spallationreactions, which were widely exploited in ISOL-type devices for the productionof exotic nuclei. Due to unknown extraction eÆciencies of these devices anda lack of information on the kinematics of the reaction products, this knowl-edge has been diÆcult to access up to now. In addition, spallation reactionscan, for example, be used for the production of neutrons in spallation neutronsources [7], and they can act as a neutron source in accelerator-driven subcrit-ical reactors which are proposed for incinerating nuclear waste [8,9] and/orfor producing energy [10].

The accuracy of existing spallation models to estimate residual productioncross sections is still far from the performance required for technical applica-tions. This is shown, for example, in Ref. [11]. One reason for the discrepancybetween experimental data and models is the lack of comprehensive experi-mental data. It has been diÆcult to systematically compare model calculationswith available experimental data in order to analyse the physical reasons forthe shortcomings of the models.

The present work reports on the complete isotopic production cross sections ofall elements from titanium (Z = 22) to lead (Z = 82) measured in the inverse-kinematics spallation reaction of 2 GeV deuterons with lead. In addition, the

1 Corresponding author. E-mail: [email protected].� (Timo Enqvist)2 Present address: Argonne National Laboratory, Argonne, IL 60439, USA

2

velocity distributions of all the produced isotopes were measured, giving thecrucial information on the reaction mechanisms involved in the production.The kinetic energies of spallation-evaporation residues and �ssion fragmentswill be given.

The main aim of the present paper is to give experimentally determined pro-duction cross sections and kinematical properties of all residues from the re-action 208Pb (1 A GeV) on deuteron. The measured data of the present workare compared with the experimental results of the reaction 208Pb (1 A GeV)on proton [4].

2 Experiment and data analysis

The experiment of the present work, 208Pb (1 A GeV) + d, was performedtogether with the experiment 208Pb (1 A GeV) + p [1,4]. The experimentalmethod and data-analysis procedure have been described in detail in Ref.[4], and thus, in the present work, only a short abstract will be given in thefollowing for describing experiment and data analysis.

As in our previous papers [1{5], the basis of the analysis was the re-constructedfull velocity distribution of each isotope. This was done by combining the dataobtained in di�erent magnetic �eld settings when scanning over the momen-tum distributions. The transmission correction could then be reduced only tothe losses due to the limited angular acceptance of the separator. The correc-tion of the angular transmission is described in Refs. [2,12]. The re-constructedfull velocity distributions also allow to disentangle reaction products formedin spallation-evaporation and spallation-�ssion reactions due to their di�erentkinematical properties.

2.1 Experimental details

The heavy-ion synchrotron SIS at GSI in Darmstadt, Germany, delivered theprimary beam of 208Pb at an energy of 1 A GeV. Reaction products were sep-arated and identi�ed by using the fragment separator FRS [13] and associateddetector equipments. The FRS is a two-stage magnetic spectrometer with adispersive intermediate image plane (S2) and an achromatic �nal image plane(S4). Two position-sensitive plastic-scintillation detectors [14], with a thick-ness of 5 mm and a vertical dimension of 80 mm and horizontal dimensions of220 mm and 200 mm, respectively, placed at S2 and S4, provided the magneticrigidities and the time-of- ight measurements.

3

In order to achieve the necessary nuclear-charge resolution for elements abovegadolinium, a pro�led aluminium degrader [15], of thickness of 5.2 g/cm2 or5.8 g/cm2, which preserves the achromacy of the spectrometer was installed atS2 . The elements below terbium were identi�ed using an ionisation chamberMUSIC [16] without the degrader.

The primary-beam intensity was continuously monitored and measured withthe beam-current monitor SEETRAM [17] from the current induced by sec-ondary electrons in 3 aluminium foils of a total thickness of 8.9 mg/cm2.

The deuteron target of a thickness of (208 � 6) mg/cm2 was realised byenclosing liquid deuterium in between thin titanium foils of a total thicknessof 36.3 mg/cm2 [18]. The contribution of the target windows to the productionrate was measured and subtracted by repeating measurements with layers ofmatter equivalent to the empty target container.

2.2 Identi�cation of elements from titanium to gadolinium

The nuclear mass number A was determined by using the equation

B� = � � AZ� c � m0

e; (1)

where B� is the magnetic rigidity of a particle and v = � � c its velocity.The magnetic rigidity was determined from the horizontal positions at theintermediate image plane S2 and at the �nal image plane S4, and the velocityfrom the time-of- ight between S2 and S4. = (1 � �2)�1=2 is the Lorentzfactor, c the velocity of light, m0 the nuclear mass unit, and e the charge ofan electron. The nuclear charge Z was deduced from the energy loss in theMUSIC detector, and in Eq. (1) events with fully stripped ions only were used(q = Z). The absolute charge calibration was performed with the help of theprimary beam (Z = 82). In the analysis, the quantity A-3Z was determinedusing Eq. (1) in order to calibrate the mass number with the help of the massnumber of the primary beam. See Ref. [4] for more details.

2.3 Identi�cation of elements from terbium to lead

The identi�cation of reaction products of elements from terbium to lead wasperformed with the help of an achromatic degrader [15] placed at S2 of theFRS. Again, by taking only the completely stripped ions all along the FRSand disregarding contaminants from secondary reactions in the layers of mat-ter at the S2 (using the method described in Ref. [4]), the nuclear charge

4

Fig. 1. Two-dimensional cluster plots of velocity versus neutron number are shownfor 12 selected elements. The three uppermost rows show the production rate withthe full target and the lowest row from the target windows. The velocity is givenin the centre-of-mass system of the primary beam in the middle of the target. Theintensity (i.e. the production rate) scale is logarithmic. In order to compare theproduction rates from the full target and from the target windows, the scale isthe same for the same element, except for ytterbium where the the target-windowproduction rate has been multiplied by a factor of 10. The distribution of ytterbiumisotopes produced in the empty target was incompletely measured. Note also thedi�erent scales in velocity in di�erent rows.

and mass calibration was performed by plotting two-dimensional spectra ofthe horizontal position at the image plane (S4) versus A=Z obtained by Eq.(1) for each magnetic �eld setting. The masses and nuclear charges in thesetwo-dimensional spectra were calibrated by counting from the centre positionwhich was known from ion-optical calculations.

5

2.4 Determination of cross sections

The velocity of a residue identi�ed in Z and A was determined using Eq.(1) with the B� value now obtained from the horizontal position at S2. Thevelocity was then transformed into the reference frame of the primary beamin the middle of the target by Lorentz transformation, taking into account theappropriate energy loss. In Fig. 1, the velocity distributions are shown for 12selected elements. The size of the symbols is proportional to the logarithmof the production rate of the isotope. An additional colour scale is introducedfor clarity. It can be seen from the distributions that the reaction productscan be attributed to di�erent reaction mechanisms, i.e. spallation-�ssion andspallation-evaporation.

The distributions in Fig. 1 (three uppermost rows) also contain a contributionfrom the titanium windows of the target. However, the production rate inFig. 1 has been corrected for dead time f� of the data-acquisition system, forthe contribution from incompletely stripped ions fq, and for counting lossesdue to secondary reactions fsec in the degrader and the scintillation detectorat S2. It is also normalised to the number of projectiles Np recorded by thebeam-intensity monitor. A calibration factor of (4500 � 140) projectiles persecond for a monitor current of 10�9 A, as deduced from the calibration withan ionisation chamber [19], was applied. The production rate R, attributed toa speci�c isotope, was obtained from the measured counting rate N of thatisotope using the equation

R =N

Np

� 1

f� � fq � fsec: (2)

The production rates de�ned by the Eq. 2 are not corrected for losses due toangular transmission ftr of the FRS and secondary reactions ftar inside theliquid-deuterium target. These and the above corrections on the productionrates are explained brie y below and more detailed in Ref [4]. The e�ectiveproduction rate Re� was obtained by subtracting the rate produced in thetitanium target windows from the production rate measured with the target�lled with liquid deuterium. The production cross section of a speci�c isotopewas then determined using the e�ective production rate Re� by the equation

� =Re�

Nt

� ftr � ftar: (3)

where Nt = dnt=dS is the number of target atoms per area.

6

Fig. 2. Main corrections applied to the data. (a) The probability that the residuesare totally stripped in both halfs of the FRS as a function of the proton numberwhen passing through the layers of matter in the FRS beam-line. (b) The survivalprobability fsec against secondary reactions as a function of the mass number. Thethicknesses of the layers of the di�erent settings are given in Table 1 in Ref. [4]. (c)The correction factor for secondary reactions ftar inside the liquid-deuterium targetfor fragmentation and for �ssion as a function of the mass number. The correctionfactor is shown for two selected elements for �ssion. (d) The angular transmissionfor backward- and forward-emitted �ssion fragments ftr as a function of the velocityof the fragments. (e) The angular transmission ftr of fragmentation products as afunction of the mass number.

2.5 Corrections and uncertainty of the data

The aim in the present experiment, as in the previous one [4], was to obtain theproduction cross section with such an accuracy that the data can be applied tothe di�erent technical applications. The aim in the statistical uncertainty wasput to 10% for cross sections above 0.1 mb. The evaluation of the statisticalerror in the production cross section of a speci�c isotope was based on theassumed systematic behaviour of the measured production cross sections. Thecross sections were presented for each N �Z -value as a function of Z, as wasdone in the case of 208Pb (1 A GeV) + p (see Fig. 7 in Ref. [4]).

7

The data of the present work were corrected as explained in Ref. [4] where amore detailed description on the corrections applied can be found. Here onlya short reminder is given.

Corrections on the production rates determined from velocity distributionsincluded dead-time of the data-acquisition system and detector eÆciencies.The dead-time was kept below 30%, and the eÆciency of the detectors wasdetermined to be higher than 98%. In addition, losses due to non-fully strippedions, due to secondary reactions in the FRS beam line, and due to limitedangular acceptance were taken into account. Fig. 2 shows the main correctionsapplied to the data in the present work.

The correction for secondary reactions in the liquid-deuterium target was per-formed both for the spallation-evaporation and spallation-�ssion products us-ing a fast simpli�ed version of the CASCABLA code [20,21]. This is describedin more detailed in the appendix of Ref. [4] where the method was applied tothe correction of �ssion residues only.

For most of the isotopes produced by spallation-evaporation reactions it waspossible to reach the desired statistical accuracy. In the present work, it wasstill more diÆcult, compared with the reaction 208Pb (1 A GeV) + p [4], todisentangle neutron-rich spallation-�ssion and spallation-evaporation productsin the range Z � 50� 60. The desired statistical accuracy of 10% for �ssionproducts was achieved above 1 mb. For most �ssion fragments, a 15% system-atic error on the production cross section was estimated due to uncertaintiesof the corrections applied. For a few neutron-de�cient isotopes the systematicuncertainty was slightly higher due to correction for secondary reactions in thetarget. For spallation residues, a systematic uncertainty was estimated being9% for the heaviest elements, and growing up to 15% for the lightest elementsaround cesium.

3 Results

3.1 Fission cross sections

The spallation-�ssion production cross sections measured in the present workfor elements from titanium to rhodium are shown in Fig. 3 and Fig. 4 as iso-topic distributions. The production cross sections of the most neutron-de�cientisotopes of elements from titanium to germanium are missing since one or twomagnetic �eld settings for those isotopes were not performed. This can also beseen as a sharp cut in the velocity distributions of the neutron-de�cient iso-topes of manganese and zinc shown in Fig. 1. There was still some production

8

Fig. 3. Isotopic production cross sections of spallation-�ssion products from thereaction 208Pb (1 A GeV) + d obtained in the present work for elements fromtitanium to arsenic. Statistical error bars are shown only. The systematic erroramounts to 15%.

by �ssion of isotopes above rhodium, but these yields are not shown in the�gures due to the diÆculty to extract them with suÆcient accuracy. In Ref.[4] the situation was similar for tellurium and higher Z values.

The measured total �ssion cross section from Pb + d at 1 A GeV for elementsfrom titanium to tellurium amounts to �f = (169 � 14) mb in the presentwork. Only the statistical uncertainty is given here. An extrapolation of the�ssion-fragment element distribution in Fig. 5(a) gives an estimation of 6 mbfor the total production cross section of elements below titanium and abovetellurium.

A Gaussian function was �tted to each isotopic distribution in Figs. 3 and 4 to

9

Fig. 4. Like Fig. 3, but now production cross sections are shown for elements fromselenium to rhodium.

reaction ��s �A �Z �A �Z �Ekin

208Pb + p 157�26y 90.7�1.0 39.6�0.5 16.1�0.8 6.6�0.3 64�4

208Pb + d 169�31y 89.6�1.1 39.0�0.7 17.4�1.0 7.3�0.5 58�5

Table 1Parameters characterising the �ssion process of the systems 208Pb (1 A GeV) + p [4]and 208Pb (1 A GeV) + d (the present work). In the table, the measured total �ssioncross section ��s (in mb), the mean value of the mass and elemental distributions,�A and �Z, and their standard deviations �A and �Z , respectively, are given. Thevalues are the mean and the standard deviations of a Gaussian �tted to the rangeof elements � 30 to 50 and masses � 65 to 115 in Figs. 5(a,b), respectively, like inRef. [4]. In addition, the last column gives the average kinetic energy (in MeV) ofa single �ssion fragment. yNote that the elements cover the range from titanium totellurium.

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Fig. 5. Integrated distributions from spallation-�ssion reactions in 208Pb (1 A GeV)+ d. The production cross sections as a function of the proton (a) and mass (d)numbers. The mean neutron-to-proton ratio (b) and proton-to-neutron ratio (e) ofisotopic distributions as a function of proton and mass numbers, respectively. (c,f) The standard deviations of the distributions. Note that data in (a) and (d) alsocontain elements above rhodium. The full line in (b) and (e) shows the position ofthe stable isotopes from Eq. (4). In (c) and (f) the data are not shown for the fullmass range due to higher uncertainties at very light and very heavy masses.

extract the parameters describing the �ssion process in the reaction 208Pb (1A GeV) + d. The results as a function of the proton and mass numbers of the�ssion fragments are shown in Fig. 5, where (a) and (d) show the productioncross section of each produced element and mass. In (b) and (c) the meanratio �N=Z and the width (�NZ ) of the distributions are shown as a functionof the proton number. In (e) and (f) the corresponding quantities are shownas a function of the mass number. Error bars in Fig. 5 represent statisticaluncertainties. The solid line in (b) and (e) shows the position of the stableisotopes. It has been obtained from the equation [22]

Zstab =A

1:98 + 0:0155A2=3: (4)

11

Z A ��s [mb] Z A ��s [mb]

22 47 0.39(0.05)(0.06) 26 56 0.88(0.13)(0.13)

22 48 0.78(0.08)(0.11) 26 57 0.97(0.09)(0.14)

22 49 0.86(0.11)(0.13) 26 58 1.07(0.11)(0.16)

22 50 0.53(0.07)(0.08) 26 59 0.80(0.05)(0.12)

22 51 0.25(0.04)(0.04) 26 60 0.50(0.08)(0.07)

22 52 0.08(0.03)(0.01) 26 61 0.31(0.03)(0.05)

26 62 0.14(0.04)(0.02)

23 49 0.52(0.07)(0.08)

23 50 0.95(0.08)(0.14) 27 58 0.68(0.05)(0.10)

23 51 1.01(0.10)(0.15) 27 59 1.17(0.08)(0.17)

23 52 0.58(0.08)(0.09) 27 60 1.12(0.11)(0.16)

23 53 0.39(0.04)(0.06) 27 61 1.04(0.06)(0.15)

23 54 0.16(0.04)(0.02) 27 62 0.80(0.09)(0.12)

27 63 0.44(0.05)(0.07)

24 52 0.80(0.07)(0.12) 27 64 0.16(0.04)(0.02)

24 53 0.99(0.10)(0.14) 27 65 0.09(0.04)(0.01)

24 54 0.87(0.09)(0.13)

24 55 0.43(0.04)(0.06) 28 60 0.67(0.10)(0.10)

24 56 0.22(0.06)(0.03) 28 61 1.00(0.08)(0.15)

24 57 0.09(0.02)(0.01) 28 62 1.53(0.12)(0.22)

28 63 1.25(0.06)(0.18)

25 54 0.90(0.07)(0.13) 28 64 1.10(0.09)(0.16)

25 55 0.99(0.10)(0.14) 28 65 0.67(0.05)(0.10)

25 56 0.82(0.10)(0.12) 28 66 0.30(0.05)(0.04)

25 57 0.69(0.04)(0.10) 28 67 0.18(0.05)(0.03)

25 58 0.35(0.08)(0.05) 28 68 0.07(0.04)(0.01)

25 59 0.16(0.02)(0.02)

29 62 0.52(0.08)(0.08)

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29 63 1.04(0.08)(0.15) 31 74 0.33(0.05)(0.05)

29 64 1.60(0.12)(0.23) 31 75 0.18(0.04)(0.03)

29 65 1.57(0.07)(0.23) 31 76 0.06(0.02)(0.01)

29 66 1.37(0.12)(0.20)

29 67 0.92(0.06)(0.14) 32 68 0.19(0.02)(0.03)

29 68 0.57(0.05)(0.08) 32 69 0.79(0.06)(0.12)

29 69 0.28(0.05)(0.04) 32 70 1.33(0.14)(0.19)

29 70 0.09(0.03)(0.01) 32 71 1.83(0.08)(0.27)

32 72 2.06(0.15)(0.30)

30 64 0.34(0.03)(0.05) 32 73 1.92(0.10)(0.28)

30 65 0.92(0.08)(0.13) 32 74 1.55(0.12)(0.23)

30 66 1.66(0.14)(0.24) 32 75 0.90(0.17)(0.13)

30 67 1.79(0.08)(0.26) 32 76 0.56(0.09)(0.08)

30 68 1.47(0.12)(0.22) 32 77 0.24(0.04)(0.04)

30 69 1.23(0.06)(0.18) 32 78 0.13(0.03)(0.02)

30 70 0.80(0.08)(0.12) 32 79 0.04(0.01)(0.01)

30 71 0.42(0.05)(0.06)

30 72 0.23(0.05)(0.03) 33 70 0.06(0.01)(0.01)

30 73 0.06(0.02)(0.01) 33 71 0.53(0.05)(0.08)

33 72 1.11(0.13)(0.16)

31 66 0.21(0.02)(0.04) 33 73 1.92(0.08)(0.28)

31 67 0.80(0.06)(0.12) 33 74 1.91(0.15)(0.28)

31 68 1.36(0.14)(0.20) 33 75 2.21(0.15)(0.32)

31 69 1.87(0.08)(0.27) 33 76 1.86(0.14)(0.27)

31 70 1.83(0.13)(0.27) 33 77 1.36(0.19)(0.20)

31 71 1.62(0.07)(0.24) 33 78 0.76(0.14)(0.11)

31 72 1.03(0.08)(0.15) 33 79 0.38(0.05)(0.06)

31 73 0.66(0.14)(0.10) 33 80 0.19(0.04)(0.03)

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33 81 0.09(0.02)(0.01) 35 86 0.06(0.02)(0.01)

34 72 0.02(0.01)(0.01) 36 77 0.17(0.04)(0.04)

34 73 0.41(0.05)(0.06) 36 78 0.84(0.11)(0.14)

34 74 1.36(0.12)(0.20) 36 79 1.60(0.14)(0.23)

34 75 1.83(0.14)(0.27) 36 80 1.99(0.14)(0.29)

34 76 2.36(0.14)(0.35) 36 81 2.54(0.21)(0.37)

34 77 2.46(0.16)(0.36) 36 82 2.65(0.16)(0.39)

34 78 2.45(0.15)(0.36) 36 83 2.67(0.23)(0.39)

34 79 1.62(0.19)(0.24) 36 84 1.93(0.21)(0.29)

34 80 1.17(0.15)(0.17) 36 85 1.20(0.07)(0.18)

34 81 0.69(0.05)(0.10) 36 86 0.59(0.06)(0.09)

34 82 0.34(0.04)(0.05) 36 87 0.33(0.04)(0.05)

34 83 0.13(0.02)(0.02) 36 88 0.11(0.03)(0.02)

34 84 0.04(0.01)(0.01) 36 89 0.05(0.01)(0.01)

35 74 0.02(0.01)(0.01) 37 79 0.14(0.02)(0.03)

35 75 0.18(0.04)(0.04) 37 80 0.57(0.10)(0.09)

35 76 0.73(0.10)(0.11) 37 81 1.33(0.14)(0.19)

35 77 1.72(0.14)(0.25) 37 82 2.13(0.14)(0.31)

35 78 2.29(0.14)(0.33) 37 83 2.41(0.27)(0.35)

35 79 2.70(0.19)(0.40) 37 84 3.36(0.16)(0.49)

35 80 2.58(0.16)(0.38) 37 85 2.87(0.28)(0.42)

35 81 2.42(0.20)(0.36) 37 86 2.36(0.25)(0.35)

35 82 1.44(0.19)(0.21) 37 87 1.53(0.16)(0.23)

35 83 0.88(0.05)(0.13) 37 88 0.79(0.07)(0.12)

35 84 0.44(0.04)(0.06) 37 89 0.41(0.06)(0.06)

35 85 0.22(0.03)(0.03) 37 90 0.24(0.03)(0.04)

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37 91 0.12(0.02)(0.02) 39 94 0.47(0.06)(0.07)

37 92 0.05(0.02)(0.01) 39 95 0.25(0.05)(0.04)

39 96 0.11(0.02)(0.02)

38 81 0.08(0.02)(0.02)

38 82 0.46(0.10)(0.08) 40 85 0.03(0.01)(0.01)

38 83 1.57(0.21)(0.23) 40 86 0.29(0.05)(0.06)

38 84 1.96(0.13)(0.29) 40 87 0.65(0.13)(0.09)

38 85 2.46(0.27)(0.36) 40 88 1.48(0.15)(0.21)

38 86 3.09(0.21)(0.45) 40 89 2.37(0.28)(0.35)

38 87 2.93(0.29)(0.43) 40 90 2.91(0.21)(0.43)

38 88 2.42(0.27)(0.36) 40 91 3.31(0.26)(0.49)

38 89 1.78(0.16)(0.26) 40 92 2.33(0.29)(0.34)

38 90 1.11(0.07)(0.16) 40 93 2.37(0.17)(0.35)

38 91 0.65(0.07)(0.10) 40 94 1.56(0.08)(0.23)

38 92 0.30(0.06)(0.04) 40 95 1.10(0.08)(0.16)

38 93 0.17(0.04)(0.03) 40 96 0.64(0.07)(0.09)

38 94 0.07(0.02)(0.01) 40 97 0.35(0.05)(0.05)

40 98 0.17(0.04)(0.02)

39 84 0.21(0.05)(0.04) 40 99 0.08(0.02)(0.01)

39 85 1.11(0.13)(0.18)

39 86 1.64(0.14)(0.24) 41 88 0.11(0.03)(0.03)

39 87 2.02(0.27)(0.30) 41 89 0.51(0.13)(0.08)

39 88 3.12(0.20)(0.46) 41 90 1.36(0.13)(0.20)

39 89 2.88(0.29)(0.42) 41 91 2.33(0.27)(0.34)

39 90 2.82(0.28)(0.42) 41 92 2.46(0.23)(0.36)

39 91 2.06(0.16)(0.30) 41 93 2.36(0.24)(0.35)

39 92 1.32(0.07)(0.20) 41 94 2.19(0.28)(0.32)

39 93 0.74(0.08)(0.11) 41 95 1.96(0.17)(0.29)

15


41 96 1.78(0.09)(0.26) 43 96 1.76(0.22)(0.26)

41 97 1.34(0.11)(0.20) 43 97 2.51(0.25)(0.37)

41 98 0.78(0.08)(0.12) 43 98 2.16(0.27)(0.32)

41 99 0.42(0.05)(0.06) 43 99 2.34(0.26)(0.35)

41 100 0.27(0.04)(0.04) 43 100 2.14(0.16)(0.32)

41 101 0.12(0.04)(0.02) 43 101 1.63(0.12)(0.24)

41 102 0.04(0.01)(0.01) 43 102 1.16(0.09)(0.17)

43 103 0.79(0.06)(0.12)

42 90 0.12(0.04)(0.03) 43 104 0.41(0.05)(0.06)

42 91 0.40(0.13)(0.07) 43 105 0.22(0.04)(0.03)

42 92 1.14(0.13)(0.17) 43 106 0.10(0.02)(0.01)

42 93 1.61(0.25)(0.23) 43 107 0.05(0.01)(0.01)

42 94 1.72(0.22)(0.25)

42 95 2.43(0.24)(0.36) 44 96 0.37(0.12)(0.06)

42 96 2.16(0.28)(0.32) 44 97 0.99(0.22)(0.14)

42 97 2.55(0.26)(0.38) 44 98 1.59(0.22)(0.23)

42 98 2.14(0.14)(0.32) 44 99 2.01(0.24)(0.30)

42 99 1.45(0.11)(0.21) 44 100 2.42(0.26)(0.36)

42 100 1.09(0.09)(0.16) 44 101 2.37(0.27)(0.35)

42 101 0.70(0.06)(0.10) 44 102 2.08(0.16)(0.31)

42 102 0.34(0.04)(0.05) 44 103 1.65(0.12)(0.24)

42 103 0.19(0.04)(0.03) 44 104 1.25(0.10)(0.18)

42 104 0.06(0.01)(0.01) 44 105 0.85(0.06)(0.13)

44 106 0.54(0.06)(0.08)

43 92 0.08(0.02)(0.02) 44 107 0.23(0.04)(0.03)

43 93 0.27(0.05)(0.05) 44 108 0.13(0.02)(0.02)

43 94 0.95(0.13)(0.14) 44 109 0.05(0.01)(0.01)

43 95 1.30(0.25)(0.19)

16


45 97 0.08(0.03)(0.02) 45 105 1.34(0.12)(0.20)

45 98 0.57(0.12)(0.09) 45 106 1.05(0.11)(0.16)

45 99 0.71(0.20)(0.10) 45 107 0.91(0.07)(0.13)

45 100 1.47(0.21)(0.21) 45 108 0.56(0.06)(0.08)

45 101 1.92(0.23)(0.28) 45 109 0.39(0.04)(0.06)

45 102 1.70(0.24)(0.25) 45 110 0.18(0.02)(0.03)

45 103 1.89(0.27)(0.28) 45 111 0.09(0.01)(0.01)

45 104 1.80(0.15)(0.27) 45 112 0.04(0.01)(0.01)

Table 2: Fission-fragment production cross sections mea-sured in the present work. The number in paren-theses gives a statistical and systematic uncertainty,respectively, of the measured value. For example,1.60(0.14)(0.23) mb means (1.60�0.14�0.23) mb where0.14 mb is statistical and 0.23 mb systematic uncertainty.

The weighted mean values of �NZ and �AZ were determined to be (2.54 � 0.21)and (1.07 � 0.08) charge units, respectively, in the present work. In Ref. [4]the value of �AZ = (1.01 � 0.09) charge units was given for 208Pb (1 A GeV)+ p. In addition, �NZ = (2.40 � 0.12) charge units was obtained for 208Pb (1A GeV) + p.

Table 1 gives the mean values and the standard deviations extracted from Figs.5(a,d). The table also gives the total �ssion cross section from the present work,given for elements from titanium to tellurium. Fission-fragment productioncross sections from titanium (Z=22) to rhodium (Z=45) are given in Table 2.

3.2 Fragmentation cross sections

Figs. 6 and 7 show the measured isotopic production cross-section distribu-tions of elements from cesium to lead produced in spallation-evaporation reac-tions. The most neutron-rich isotopes of elements from rhenium to gold havebeen removed due to the presense of the primary beam causing an unaccuratedetermination of cross sections of these isotopes.

The secondary-reaction correction of 30% inside the liquid-deuterium target

17

Fig. 6. Production cross sections of spallation-evaporation products from the re-action 208Pb (1 A GeV) + d obtained in the present work are shown as isotopicdistributions for elements from cesium to dysprosium. Error bars shown correspondto statistical uncertainties. The additional systematic uncertainty amounts to 13%in average.

was taken as a criterion to select the lightest element produced by spallation-evaporation reaction for which we give individual isotopic cross sections. Ascan be seen from Fig. 2(c), the 30% level is achieved around mass number 115,and cesium is the lightest element where all the produced isotopes have massnumbers higher than 115.

The elements lighter than cesium produced by spallation-evaporation reactionsin the present work could only be determined with relative large uncertainties.The range from palladium to xenon is, however, included in Fig. 12 to give acomplete survey of the isotopic production on the chart of the nuclides.

18

Fig. 7. Like Fig. 6, but now production cross sections are shown for elements fromholmium to lead. Here the systematic uncertainty amounts to 10% in average.

In the reaction 208Pb (1 A GeV) + p the most important contribution to theisotopic production was observed to come from the heaviest elements just be-low lead with the contribution from the lightest elements being rather small.The total spallation-evaporation residue cross section for elements from prome-thium to lead was determined to be �frag = (1.68 � 0.22) b for Pb (1 A GeV)+ p [4]. The total spallation-evaporation cross section of the present work

19

was determined to be �frag = (1.91 � 0.24) b for elements from cesium tolead. Also here the main contribution comes from the elements close to lead.The �ve heaviest elements take nearly 50% of the total spallation-evaporationcross section, which can also be seen in Fig. 8(a). An estimation of 50 mb wasobtained for the sum of the production cross sections of elements from xenondown to hydrogen using an exponential extrapolation in Fig. 8(a).

The mass distribution of fragmentation products is shown in Fig. 8(b) withfull symbols for the data obtained in the present work, and with open symbolsfor the reaction 208Pb (1 A GeV) + p [4]. As was the case in the reaction208Pb (1 A GeV) + p [4], due to a tiny blind spot in the scintillation detectorat S2, also here the cross-section values of some neutron-rich lead isotopes(N = 109; 112; 115; 118; 121; 124) have exceptionally large uncertainties. Thee�ect is visible only when the velocity distribution is very narrow, and it hasthus no e�ect for lighter elements. The production cross sections of the abovementioned lead isotopes were corrected for this e�ect and their error bars wereincreased accordingly.

Spallation-residue production cross sections from the present work for elementsfrom cesium to lead are given in Table 3.

20

Fig. 8. Element distribution (a) and mass distribution (b) of spallation-evaporationresidues. 208Pb (1 A GeV) + d (the present work) as full symbols, and 208Pb (1 AGeV) + p [4] as open symbols. Only statistical uncertainties are shown.

21

Z A �frag [mb] Z A �fag [mb]

55 118 0.011(0.003)(0.002) 56 133 0.096(0.008)(0.013)

55 119 0.049(0.003)(0.007) 56 134 0.048(0.005)(0.006)

55 120 0.186(0.008)(0.028) 56 135 0.023(0.003)(0.003)

55 121 0.462(0.046)(0.069) 56 136 0.010(0.004)(0.001)

55 122 0.826(0.060)(0.121)

55 123 1.117(0.062)(0.163) 57 122 0.004(0.001)(0.001)

55 124 1.203(0.054)(0.173) 57 123 0.022(0.003)(0.003)

55 125 1.087(0.047)(0.155) 57 124 0.112(0.007)(0.016)

55 126 0.840(0.051)(0.118) 57 125 0.329(0.028)(0.047)

55 127 0.541(0.021)(0.075) 57 126 0.736(0.042)(0.104)

55 128 0.297(0.021)(0.041) 57 127 1.212(0.055)(0.169)

55 129 0.157(0.017)(0.021) 57 128 1.581(0.058)(0.218)

55 130 0.090(0.012)(0.012) 57 129 1.526(0.059)(0.208)

55 131 0.042(0.008)(0.006) 57 130 1.333(0.064)(0.180)

57 131 1.013(0.038)(0.135)

56 120 0.006(0.002)(0.001) 57 132 0.701(0.030)(0.092)

56 121 0.035(0.003)(0.005) 57 133 0.424(0.021)(0.055)

56 122 0.145(0.007)(0.021) 57 134 0.258(0.015)(0.033)

56 123 0.405(0.035)(0.059) 57 135 0.121(0.015)(0.015)

56 124 0.806(0.049)(0.116) 57 136 0.065(0.005)(0.008)

56 125 1.199(0.060)(0.171) 57 137 0.028(0.003)(0.004)

56 126 1.357(0.056)(0.191)

56 127 1.335(0.053)(0.186) 58 124 0.002(0.001)(0.001)

56 128 1.066(0.059)(0.147) 58 125 0.015(0.002)(0.002)

56 129 0.765(0.030)(0.104) 58 126 0.076(0.005)(0.011)

56 130 0.496(0.025)(0.067) 58 127 0.256(0.027)(0.036)

56 131 0.309(0.019)(0.041) 58 128 0.648(0.039)(0.089)

56 132 0.177(0.014)(0.023) 58 129 1.197(0.054)(0.163)

22

Z A �frag [mb] Z A �frag [mb]

58 130 1.669(0.058)(0.225) 59 142 0.024(0.005)(0.003)

58 131 1.834(0.068)(0.245)

58 132 1.639(0.072)(0.216) 60 129 0.005(0.001)(0.001)

58 133 1.290(0.047)(0.168) 60 130 0.032(0.004)(0.004)

58 134 0.901(0.035)(0.116) 60 131 0.141(0.008)(0.019)

58 135 0.588(0.025)(0.075) 60 132 0.423(0.016)(0.056)

58 136 0.337(0.019)(0.042) 60 133 0.997(0.035)(0.130)

58 137 0.178(0.016)(0.022) 60 134 1.716(0.069)(0.221)

58 138 0.089(0.007)(0.011) 60 135 2.282(0.081)(0.291)

58 139 0.039(0.005)(0.005) 60 136 2.357(0.098)(0.297)

58 140 0.016(0.005)(0.002) 60 137 2.190(0.083)(0.273)

58 141 0.007(0.004)(0.001) 60 138 1.643(0.071)(0.202)

60 139 1.160(0.076)(0.141)

59 127 0.009(0.002)(0.001) 60 140 0.698(0.056)(0.084)

59 128 0.051(0.004)(0.007) 60 141 0.398(0.028)(0.047)

59 129 0.183(0.010)(0.025) 60 142 0.186(0.026)(0.022)

59 130 0.558(0.022)(0.075) 60 143 0.088(0.022)(0.010)

59 131 1.121(0.041)(0.150) 60 144 0.037(0.017)(0.004)

59 132 1.704(0.060)(0.225) 60 145 0.015(0.005)(0.002)

59 133 2.056(0.073)(0.268)

59 134 2.092(0.081)(0.270) 61 131 0.003(0.002)(0.001)

59 135 1.674(0.059)(0.213) 61 132 0.019(0.005)(0.002)

59 136 1.220(0.045)(0.154) 61 133 0.093(0.006)(0.012)

59 137 0.840(0.043)(0.105) 61 134 0.332(0.013)(0.043)

59 138 0.500(0.025)(0.062) 61 135 0.829(0.032)(0.106)

59 139 0.266(0.018)(0.032) 61 136 1.660(0.072)(0.209)

59 140 0.134(0.008)(0.016) 61 137 2.387(0.087)(0.297)

59 141 0.063(0.005)(0.007) 61 138 2.895(0.118)(0.356)

23


61 139 2.635(0.106)(0.320) 63 138 0.159(0.009)(0.020)

61 140 2.159(0.100)(0.259) 63 139 0.499(0.023)(0.061)

61 141 1.583(0.093)(0.188) 63 140 1.340(0.065)(0.161)

61 142 1.002(0.067)(0.117) 63 141 2.409(0.087)(0.285)

61 143 0.604(0.036)(0.070) 63 142 3.461(0.135)(0.405)

61 144 0.288(0.029)(0.033) 63 143 3.876(0.145)(0.448)

61 145 0.141(0.031)(0.016) 63 144 3.496(0.145)(0.399)

61 146 0.068(0.028)(0.008) 63 145 2.780(0.123)(0.313)

61 147 0.027(0.008)(0.003) 63 146 1.784(0.085)(0.198)

61 148 0.012(0.008)(0.001) 63 147 1.095(0.048)(0.120)

63 148 0.658(0.050)(0.071)

62 135 0.063(0.006)(0.008) 63 149 0.372(0.034)(0.040)

62 136 0.227(0.010)(0.029) 63 150 0.203(0.031)(0.021)

62 137 0.687(0.028)(0.086) 63 151 0.095(0.014)(0.010)

62 138 1.474(0.068)(0.181) 63 152 0.045(0.008)(0.005)

62 139 2.469(0.089)(0.300)

62 140 3.162(0.126)(0.379) 64 140 0.098(0.007)(0.012)

62 141 3.266(0.127)(0.387) 64 141 0.384(0.021)(0.046)

62 142 2.772(0.124)(0.324) 64 142 1.026(0.059)(0.120)

62 143 2.116(0.105)(0.244) 64 143 2.305(0.084)(0.266)

62 144 1.387(0.075)(0.158) 64 144 3.527(0.136)(0.402)

62 145 0.772(0.040)(0.087) 64 145 4.594(0.167)(0.517)

62 146 0.441(0.036)(0.049) 64 146 4.303(0.169)(0.478)

62 147 0.217(0.032)(0.024) 64 147 3.170(0.136)(0.347)

62 148 0.107(0.030)(0.012) 64 148 2.218(0.096)(0.240)

62 149 0.052(0.014)(0.006) 64 149 1.615(0.063)(0.172)

64 150 0.983(0.064)(0.103)

63 137 0.034(0.006)(0.004) 64 151 0.591(0.038)(0.061)

24


64 152 0.325(0.034)(0.033) 66 145 0.181(0.014)(0.020)

64 153 0.176(0.021)(0.018) 66 146 0.665(0.042)(0.074)

64 154 0.084(0.013)(0.008) 66 147 1.873(0.061)(0.205)

64 155 0.034(0.007)(0.003) 66 148 3.793(0.121)(0.410)

66 149 5.049(0.156)(0.538)

65 141 0.004(0.002)(0.001) 66 150 5.316(0.172)(0.558)

65 142 0.057(0.004)(0.007) 66 151 5.027(0.164)(0.520)

65 143 0.281(0.015)(0.032) 66 152 4.300(0.134)(0.439)

65 144 0.926(0.046)(0.106) 66 153 3.441(0.104)(0.346)

65 145 2.150(0.068)(0.242) 66 154 2.506(0.089)(0.248)

65 146 3.884(0.124)(0.431) 66 155 1.574(0.054)(0.154)

65 147 5.299(0.163)(0.580) 66 156 0.926(0.040)(0.089)

65 148 5.274(0.169)(0.570) 66 157 0.494(0.032)(0.047)

65 149 4.219(0.142)(0.449) 66 158 0.274(0.015)(0.026)

65 150 3.244(0.106)(0.341) 66 159 0.122(0.009)(0.011)

65 151 2.411(0.076)(0.250) 66 160 0.051(0.013)(0.005)

65 152 1.614(0.067)(0.165) 66 161 0.016(0.007)(0.001)

65 153 1.068(0.040)(0.107) 66 162 0.006(0.001)(0.001)

65 154 0.643(0.032)(0.064)

65 155 0.313(0.025)(0.030) 67 145 0.001(0.001)(0.001)

65 156 0.163(0.012)(0.016) 67 146 0.019(0.004)(0.002)

65 157 0.072(0.006)(0.007) 67 147 0.105(0.014)(0.012)

65 158 0.029(0.011)(0.003) 67 148 0.477(0.040)(0.052)

65 159 0.010(0.003)(0.001) 67 149 1.494(0.051)(0.159)

65 160 0.004(0.002)(0.001) 67 150 3.139(0.104)(0.330)

67 151 4.677(0.147)(0.484)

66 143 0.004(0.003)(0.001) 67 152 5.788(0.185)(0.590)

66 144 0.034(0.004)(0.004) 67 153 5.850(0.186)(0.588)

25


67 154 5.132(0.158)(0.508) 68 162 0.785(0.026)(0.071)

67 155 4.670(0.139)(0.455) 68 163 0.400(0.028)(0.036)

67 156 3.386(0.112)(0.325) 68 164 0.201(0.015)(0.018)

67 157 2.304(0.076)(0.218) 68 165 0.093(0.024)(0.008)

67 158 1.481(0.055)(0.138) 68 166 0.039(0.005)(0.004)

67 159 0.911(0.040)(0.083) 68 167 0.015(0.006)(0.001)

67 160 0.455(0.019)(0.041) 68 168 0.004(0.002)(0.001)

67 161 0.237(0.017)(0.021) 68 169 0.002(0.003)(0.001)

67 162 0.106(0.013)(0.010)

67 163 0.045(0.017)(0.004) 69 150 0.004(0.002)(0.001)

67 164 0.017(0.006)(0.002) 69 151 0.033(0.013)(0.003)

67 165 0.005(0.003)(0.001) 69 152 0.179(0.024)(0.018)

69 153 0.695(0.027)(0.070)

68 147 0.001(0.001)(0.001) 69 154 1.822(0.060)(0.180)

68 148 0.008(0.004)(0.001) 69 155 3.406(0.109)(0.332)

68 149 0.067(0.012)(0.007) 69 156 4.917(0.159)(0.472)

68 150 0.307(0.039)(0.032) 69 157 6.104(0.186)(0.577)

68 151 1.070(0.041)(0.111) 69 158 6.660(0.196)(0.619)

68 152 2.481(0.087)(0.253) 69 159 6.355(0.187)(0.581)

68 153 3.989(0.128)(0.401) 69 160 5.760(0.175)(0.518)

68 154 5.394(0.175)(0.534) 69 161 4.331(0.132)(0.383)

68 155 6.529(0.203)(0.637) 69 162 3.080(0.098)(0.279)

68 156 5.999(0.182)(0.576) 69 163 2.057(0.067)(0.186)

68 157 5.730(0.169)(0.541) 69 164 1.157(0.037)(0.105)

68 158 4.837(0.150)(0.450) 69 165 0.683(0.035)(0.062)

68 159 3.254(0.104)(0.298) 69 166 0.324(0.017)(0.029)

68 160 2.257(0.076)(0.203) 69 167 0.166(0.023)(0.015)

68 161 1.488(0.053)(0.132) 69 168 0.075(0.006)(0.007)

26


69 169 0.031(0.009)(0.003) 71 155 0.004(0.002)(0.001)

69 170 0.015(0.007)(0.002) 71 156 0.040(0.016)(0.004)

69 171 0.005(0.003)(0.001) 71 157 0.206(0.009)(0.019)

71 158 0.783(0.026)(0.073)

70 152 0.002(0.002)(0.001) 71 159 1.909(0.059)(0.175)

70 153 0.014(0.008)(0.002) 71 160 3.641(0.116)(0.328)

70 154 0.094(0.009)(0.009) 71 161 5.829(0.175)(0.516)

70 155 0.403(0.013)(0.039) 71 162 7.435(0.219)(0.674)

70 156 1.271(0.039)(0.122) 71 163 7.749(0.228)(0.702)

70 157 2.765(0.085)(0.261) 71 164 7.726(0.234)(0.700)

70 158 4.658(0.148)(0.433) 71 165 7.193(0.214)(0.652)

70 159 6.291(0.188)(0.576) 71 166 5.022(0.154)(0.455)

70 160 7.141(0.209)(0.643) 71 167 3.867(0.120)(0.350)

70 161 7.290(0.215)(0.645) 71 168 2.832(0.086)(0.257)

70 162 7.169(0.216)(0.650) 71 169 1.761(0.059)(0.160)

70 163 5.592(0.167)(0.507) 71 170 1.051(0.037)(0.095)

70 164 4.160(0.129)(0.377) 71 171 0.616(0.030)(0.056)

70 165 3.048(0.095)(0.276) 71 172 0.305(0.018)(0.028)

70 166 1.816(0.057)(0.165) 71 173 0.154(0.011)(0.014)

70 167 1.086(0.043)(0.098) 71 174 0.077(0.012)(0.007)

70 168 0.640(0.025)(0.058) 71 175 0.038(0.007)(0.003)

70 169 0.297(0.025)(0.027) 71 176 0.012(0.005)(0.002)

70 170 0.152(0.013)(0.014) 71 177 0.004(0.003)(0.001)

70 171 0.075(0.010)(0.007)

70 172 0.030(0.012)(0.003) 72 158 0.014(0.009)(0.001)

70 173 0.013(0.006)(0.002) 72 159 0.102(0.007)(0.009)

70 174 0.005(0.003)(0.001) 72 160 0.447(0.016)(0.040)

72 161 1.272(0.042)(0.113)

27


72 162 2.771(0.091)(0.251) 73 168 8.893(0.265)(0.806)

72 163 4.638(0.142)(0.420) 73 169 9.273(0.274)(0.840)

72 164 6.799(0.202)(0.616) 73 170 7.798(0.232)(0.707)

72 165 7.568(0.223)(0.686) 73 171 6.977(0.209)(0.632)

72 166 8.342(0.251)(0.756) 73 172 5.347(0.158)(0.484)

72 167 7.896(0.234)(0.715) 73 173 3.963(0.120)(0.359)

72 168 6.533(0.196)(0.592) 73 174 2.668(0.081)(0.242)

72 169 5.191(0.158)(0.470) 73 175 1.754(0.061)(0.159)

72 170 3.987(0.119)(0.361) 73 176 1.075(0.037)(0.097)

72 171 2.470(0.078)(0.224) 73 177 0.627(0.021)(0.057)

72 172 1.625(0.052)(0.147) 73 178 0.337(0.027)(0.031)

72 173 0.933(0.039)(0.085) 73 179 0.177(0.025)(0.016)

72 174 0.558(0.023)(0.051) 73 180 0.088(0.008)(0.008)

72 175 0.275(0.013)(0.025) 73 181 0.044(0.011)(0.004)

72 176 0.145(0.018)(0.013) 73 182 0.017(0.009)(0.002)

72 177 0.075(0.016)(0.007)

72 178 0.029(0.008)(0.003) 74 162 0.002(0.001)(0.001)

72 179 0.012(0.005)(0.002) 74 163 0.023(0.007)(0.002)

72 180 0.003(0.002)(0.001) 74 164 0.112(0.011)(0.010)

74 165 0.387(0.022)(0.035)

73 160 0.004(0.004)(0.001) 74 166 1.174(0.052)(0.106)

73 161 0.049(0.007)(0.004) 74 167 2.536(0.079)(0.230)

73 162 0.229(0.012)(0.021) 74 168 4.564(0.139)(0.413)

73 163 0.750(0.029)(0.068) 74 169 6.893(0.204)(0.625)

73 164 1.800(0.067)(0.163) 74 170 8.937(0.266)(0.810)

73 165 3.605(0.111)(0.327) 74 171 9.253(0.273)(0.838)

73 166 5.932(0.177)(0.537) 74 172 9.503(0.281)(0.861)

73 167 7.366(0.218)(0.667) 74 173 8.557(0.253)(0.775)

28


74 174 7.158(0.210)(0.649) 75 180 3.078(0.093)(0.279)

74 175 5.378(0.160)(0.487) 75 181 2.281(0.068)(0.207)

74 176 4.236(0.125)(0.384) 75 182 1.374(0.049)(0.124)

74 177 2.923(0.093)(0.265) 75 183 0.881(0.039)(0.080)

74 178 1.985(0.062)(0.180) 75 184 0.522(0.018)(0.047)

74 179 1.220(0.037)(0.111) 75 185 0.290(0.018)(0.026)

74 180 0.755(0.036)(0.068) 75 186 0.152(0.035)(0.014)

74 181 0.400(0.031)(0.036)

74 182 0.232(0.012)(0.021) 76 167 0.001(0.003)(0.001)

74 183 0.138(0.012)(0.013) 76 168 0.013(0.008)(0.001)

74 184 0.061(0.032)(0.006) 76 169 0.065(0.015)(0.006)

74 185 0.021(0.010)(0.002) 76 170 0.240(0.032)(0.022)

76 171 0.754(0.036)(0.068)

75 165 0.005(0.002)(0.001) 76 172 1.906(0.070)(0.173)

75 166 0.037(0.010)(0.003) 76 173 3.492(0.110)(0.316)

75 167 0.166(0.018)(0.015) 76 174 5.843(0.179)(0.529)

75 168 0.542(0.038)(0.049) 76 175 7.660(0.228)(0.694)

75 169 1.431(0.051)(0.130) 76 176 8.991(0.267)(0.815)

75 170 2.925(0.095)(0.265) 76 177 10.420(0.307)(0.944)

75 171 5.043(0.151)(0.457) 76 178 9.450(0.278)(0.856)

75 172 7.029(0.211)(0.637) 76 179 8.571(0.252)(0.777)

75 173 8.248(0.245)(0.747) 76 180 7.931(0.232)(0.719)

75 174 9.159(0.272)(0.830) 76 181 6.073(0.180)(0.550)

75 175 9.101(0.268)(0.825) 76 182 4.911(0.145)(0.445)

75 176 8.139(0.239)(0.737) 76 183 3.927(0.115)(0.356)

75 177 6.934(0.205)(0.628) 76 184 2.592(0.081)(0.235)

75 178 5.803(0.170)(0.526) 76 185 1.740(0.059)(0.158)

75 179 4.357(0.132)(0.395) 76 186 1.220(0.038)(0.110)

29


76 187 0.730(0.028)(0.066) 77 192 0.506(0.027)(0.046)

76 188 0.465(0.040)(0.042) 77 193 0.316(0.029)(0.029)

76 189 0.275(0.014)(0.025)

76 190 0.144(0.024)(0.013) 78 173 0.005(0.003)(0.001)

76 191 0.055(0.026)(0.005) 78 174 0.022(0.007)(0.002)

78 175 0.102(0.028)(0.009)

77 170 0.002(0.004)(0.001) 78 176 0.363(0.046)(0.033)

77 171 0.016(0.009)(0.001) 78 177 1.015(0.055)(0.092)

77 172 0.097(0.030)(0.009) 78 178 2.171(0.091)(0.197)

77 173 0.332(0.028)(0.030) 78 179 3.854(0.128)(0.349)

77 174 0.943(0.050)(0.085) 78 180 5.493(0.174)(0.498)

77 175 2.094(0.076)(0.190) 78 181 7.387(0.227)(0.669)

77 176 3.838(0.128)(0.348) 78 182 9.137(0.273)(0.828)

77 177 5.864(0.180)(0.531) 78 183 9.439(0.279)(0.855)

77 178 7.588(0.228)(0.687) 78 184 10.095(0.297)(0.915)

77 179 9.222(0.273)(0.835) 78 185 10.204(0.300)(0.924)

77 180 9.822(0.289)(0.890) 78 186 8.898(0.261)(0.806)

77 181 9.649(0.283)(0.874) 78 187 8.915(0.262)(0.808)

77 182 9.293(0.273)(0.842) 78 188 7.607(0.224)(0.689)

77 183 8.915(0.262)(0.808) 78 189 5.979(0.178)(0.542)

77 184 7.196(0.211)(0.652) 78 190 5.006(0.147)(0.454)

77 185 6.240(0.184)(0.565) 78 191 4.090(0.121)(0.371)

77 186 5.074(0.151)(0.460) 78 192 2.694(0.089)(0.244)

77 187 3.636(0.112)(0.329) 78 193 2.226(0.066)(0.202)

77 188 2.626(0.079)(0.238) 78 194 1.647(0.053)(0.149)

77 189 1.868(0.057)(0.169) 78 195 0.984(0.039)(0.089)

77 190 1.244(0.054)(0.113) 78 196 0.464(0.073)(0.042)

77 191 0.849(0.027)(0.077)

30


79 176 0.001(0.001)(0.001) 80 182 0.284(0.055)(0.026)

79 177 0.015(0.011)(0.001) 80 183 0.757(0.070)(0.069)

79 178 0.095(0.046)(0.009) 80 184 1.619(0.081)(0.147)

79 179 0.344(0.045)(0.031) 80 185 3.099(0.117)(0.281)

79 180 0.956(0.069)(0.087) 80 186 5.191(0.164)(0.470)

79 181 2.100(0.090)(0.190) 80 187 6.951(0.209)(0.630)

79 182 3.525(0.122)(0.319) 80 188 9.161(0.270)(0.830)

79 183 5.414(0.175)(0.490) 80 189 11.296(0.333)(1.023)

79 184 7.514(0.227)(0.681) 80 190 12.986(0.380)(1.177)

79 185 9.237(0.274)(0.837) 80 191 13.713(0.401)(1.242)

79 186 10.419(0.306)(0.944) 80 192 15.322(0.448)(1.388)

79 187 11.639(0.342)(1.054) 80 193 14.611(0.428)(1.324)

79 188 11.674(0.341)(1.058) 80 194 14.202(0.415)(1.287)

79 189 11.985(0.351)(1.086) 80 195 15.019(0.438)(1.361)

79 190 11.688(0.342)(1.059) 80 196 12.331(0.363)(1.117)

79 191 10.310(0.303)(0.934) 80 197 11.510(0.336)(1.043)

79 192 9.218(0.270)(0.835) 80 198 10.820(0.316)(0.980)

79 193 8.150(0.238)(0.738) 80 199 9.159(0.269)(0.830)

79 194 6.850(0.205)(0.621) 80 200 7.317(0.215)(0.663)

79 195 5.279(0.154)(0.478) 80 201 6.005(0.202)(0.544)

79 196 4.286(0.127)(0.388) 80 202 3.555(0.175)(0.322)

79 197 3.408(0.103)(0.309) 80 203 1.917(0.056)(0.174)

79 198 2.187(0.068)(0.198)

79 199 1.527(0.109)(0.138) 81 182 0.001(0.001)(0.001)

81 183 0.005(0.003)(0.002)

80 179 0.001(0.001)(0.001) 81 184 0.032(0.016)(0.003)

80 180 0.017(0.008)(0.002) 81 185 0.127(0.045)(0.012)

80 181 0.072(0.027)(0.007) 81 186 0.431(0.071)(0.039)

31


81 187 1.038(0.081)(0.094) 82 187 0.005(0.003)(0.001)

81 188 1.969(0.088)(0.178) 82 188 0.037(0.019)(0.003)

81 189 3.540(0.118)(0.321) 82 189 0.149(0.067)(0.013)

81 190 5.751(0.173)(0.521) 82 190 0.385(0.074)(0.035)

81 191 7.638(0.228)(0.692) 82 191 0.977(0.068)(0.089)

81 192 9.324(0.273)(0.845) 82 192 2.038(0.075)(0.185)

81 193 12.395(0.363)(1.123) 82 193 2.891(0.096)(0.262)

81 194 12.985(0.380)(1.176) 82 194 4.324(0.129)(0.392)

81 195 15.372(0.450)(1.393) 82 195 6.419(0.191)(0.582)

81 196 16.935(0.494)(1.534) 82 196 7.310(0.214)(0.662)

81 197 17.129(0.500)(1.552) 82 197 9.634(0.566)(0.873)

81 198 18.109(0.530)(1.641) 82 198 12.207(0.357)(1.106)

81 199 18.116(0.528)(1.641) 82 199 13.069(0.382)(1.184)

81 200 17.009(0.497)(1.541) 82 200 16.716(0.979)(1.515)

81 201 20.122(0.587)(1.823) 82 201 19.709(0.575)(1.786)

81 202 20.630(0.602)(1.869) 82 202 20.270(0.592)(1.836)

81 203 17.977(0.535)(1.629) 82 203 23.946(1.397)(2.170)

81 204 16.166(0.492)(1.465) 82 204 31.311(0.913)(2.837)

82 205 34.039(0.999)(3.084)

82 206 43.593(2.554)(3.950)

82 207 70.805(2.065)(6.415)

Table 3: Spallation-evaporation residue production crosssections for Z = 55 - 82 measured in the presentwork. The number in parentheses gives a statisticaland systematic uncertainty, respectively, of the mea-sured value. For example, 5.316(0.172)(0.558) mb means(5.316�0.172�0.558) mb where 0.172 mb is statisticaland 0.558 mb systematic uncertainty.

32

3.3 Velocities of �ssion fragments

The averaged mean velocities of �ssion fragments and the estimated �ssioningelements were deduced in the present work by using the procedure describedin detail in Refs. [4,23]. The mean velocity values induced in the �ssion pro-cess are shown in Fig. 9(a) as a function of the proton number of the �ssionfragment. The full symbols show the data obtained in the present work forlead on deuteron, and the open symbols are taken for lead on proton from [4]for comparison.

The total kinetic energy TKE in �ssion can be expressed, provided that theexcitation energy of the �ssioning system is high enough that shell e�ects arewashed out, by the equation

TKE =Z1Z2e

2

D(5)

with

D = r0A1=31 (1 +

2�13) + r0A

1=32 (1 +

2�23) + d; (6)

where A1, A2, Z1, and Z2 denote the mass and charge numbers of a pair of�ssion fragments. The parameters (r0 = 1:16 fm, d = 2:0 fm, and �1 = �2 =0:625) were taken from Refs. [24,25].

The three solid lines in Fig. 9(a) indicating the element of the �ssioning systemcontributing to the production of a �xed �ssion fragment were calculated withthe help of Eqs. (5) and (6). It was assumed in the calculations that the�ssioning nucleus and the observed �ssion fragment have the same A=Z ratio.This also �xes the A=Z ratio of the second fragment, provided that the neutronevaporation after �ssion was neglected. The mean mass number �A1(Z1) of theobserved �ssion fragment Z1 was taken from measured data (see Fig. 5(b)).

3.4 Spallation-residue momentum distribution

The mean longitudinal momentum �pk(Z;A) and the width ��p(Z;A) of themomentum distribution of an isotope (Z;A) with respect to the primary beamcould be determined from the corresponding velocity distributions by usingthe non-relativistic equations

�pk(Z;A) = Am0 � �vk(Z;A); (7)

33

Fig. 9. (a) Measured �ssion-fragment mean velocities as a function of their protonnumber. Full symbols show the data of the present work for 208Pb (1 A GeV) + d,and open symbols for 208Pb (1 A GeV) + p [4]. The full lines indicate the calculatedvelocity values corresponding to �ssion from lead (Z�s = 82), osmium (Z�s = 76)and ytterbium (Z�s = 70) isotopes with the same �A=Z ratio as the observed frag-ment. The in uence of neutron evaporation after �ssion on the calculated fragmentvelocities was neglected. It would enter only weakly into the calculation by insert-ing the pre-neutron-emission mass values A1 and A2 into Eq. (6). Only statisticaluncertainties are shown. (b) Measured �ssion-fragment mean kinetic energies as afunction of the proton number as full symbols for the data of the present work(208Pb (1 A GeV) + d) and as open symbols for the data of Ref. [4] (208Pb (1 AGeV) + p). Error bars shown in the �gure contain statistical uncertainties only.

��p(Z;A) = Am0 � ��v(Z;A) (8)

since velocities were transformed into the center-of-mass system. m0 is theatomic mass unit.

34

The average mean value and the width of the longitudinal-momentum dis-tribution were taken from Eqs. (7) and (8) as weighted mean by using theproduction cross section �(Z;A) of the isotope (Z;A) as a weighting factor.

Fig. 10 shows the average mean values and standard deviations of the mo-mentum distributions of spallation residues as a function of mass numberfrom reactions 208Pb (1 A GeV) + p ([4], open symbols) and 208Pb (1 A GeV)+ d (the present work, full symbols). The data are compared with the em-pirical systematics proposed by Morrissey [26] as the solid line, and with thepredictions of the Goldhaber model [27] as the dashed line. The equations forlongitudinal momentum and standard deviation of the momentum distribu-tion of the Morrissey systematics [26] are expressed as a function of the massloss �A as

�pk(A) = � 8:0

0:589��A; (9)

��p(A) =150p3�p�A: (10)

According to the Goldhaber model [27] the standard deviation of the momen-tum distribution is calculated by using the equation

��p(A) =pFp5�sAf ��AAp � 1

; (11)

where �A is the mass loss, Af the mass number of the fragment, and Ap themass of the projectile. pF is the Fermi momentum; pF = 265 MeV/c was usedhere.

3.5 Kinetic energies

In the present work, the kinetic energy of a �ssion fragment obtained in the�ssion process was calculated, in the frame of the �ssioning nucleus, by usingthe equation

�ECM(Z) =1

2� �A(Z)m0 � �v2CM; (12)

where m0 is the atomic mass unit, and �A(Z) the most probable mass numberfor given nuclear charge Z obtained from the measured isotopic distributions.The average �ssion-fragment velocity �vCM(Z) was taken from Fig. 9(a). Thekinetic energies are shown in Fig. 9(b) as a function of the proton number for

35

Fig. 10. Average mean values (a) and standard deviations (b) of the momentumdistribution of spallation residues induced in the reactions of 208Pb (1 A GeV) +p [4] (open symbols) and 208Pb (1 A GeV) + d (the present work, full symbols).The solid line indicates the empirical systematics derived by Morrissey [26] for themean value and the width, respectively, and the dashed line the predictions of theGoldhaber model [27].

the reaction 208Pb (1 A GeV) + d of the present work with full symbols andfor the reaction 208Pb (1 A GeV) + p of Ref. [4] with open symbols.

The average kinetic energy of a �ssion fragment in the frame of the projectilecan be calculated by the equation

�Ekin(Z) =1

2� �A(Z)m0 � (�v2�s + �v2CM); (13)

36

Z �Ekin [MeV] Z �Ekin [MeV] Z �Ekin [MeV]

22 58.2 � 1.2 35 57.6 � 1.1 48 52.4 � 1.3

23 58.0 � 1.3 36 57.9 � 1.1 49 51.6 � 1.5

24 55.6 � 1.3 37 57.6 � 1.3 50 48.3 � 1.3

25 56.7 � 1.2 38 60.4 � 1.2 51 47.0 � 1.2

26 56.2 � 1.2 39 61.0 � 1.6 52 43.4 � 1.4

27 57.9 � 1.2 40 59.2 � 1.6 53 42.6 � 1.0

28 59.3 � 1.2 41 59.3 � 1.6 54 38.5 � 0.9

29 58.7 � 1.0 42 56.9 � 1.3 55 36.9 � 0.9

30 57.3 � 0.9 43 58.5 � 1.4

31 57.6 � 1.0 44 59.8 � 1.7

32 56.8 � 1.0 45 58.9 � 1.6

33 58.6 � 1.1 46 57.5 � 1.4

34 58.3 � 1.5 47 55.0 � 1.5

Table 4The mean kinetic-energy values of single �ssion fragments with an atomic numberZ, measured in the present work.

when an isotropic velocity distribution is assumed. �v�s(Z) is the average veloc-ity of the �ssioning element with respect to the primary beam. The di�erencein kinetic energy between Eqs. (13) and (12) is very small, and cannot bedistinguished with the resolution of the present experiment. Table 4 givesthe average kinetic energy �Ekin(Z) of a �ssion fragment of atomic number Zmeasured in the present work.

The average kinetic energy of the spallation recoil product (Z;A) was, in thepresent work, determined by the same way as explained in Ref. [4], by usingthe equation

�Ekin(Z;A) =1

2Am0(�v

2CM + 3��2CM); (14)

where �vCM(Z;A) is an average velocity and ��CM(Z;A) the standard deviationof the measured velocity distributions shown in Fig. 1. The average kineticenergies as a function of the proton and mass numbers, respectively, werethen obtained as a weighted mean of Eq. (14) using the production crosssection of the isotope as a weighting factor. The kinetic energies of spallation-evaporation residues measured in the present work are plotted in Fig. 11(a, b)with full symbols. They are compared, as open symbols, with kinetic energiesof spallation residues from Ref. [4] for 208Pb (1 A GeV) + p. In Fig. 11, only

37

Fig. 11. Mean spallation-residue kinetic energies as a function of the proton (a) andmass (b) numbers as full symbols for the data of the present work. Error bars shownin the �gure contain statistical uncertainties only. For comparison, kinetic-energydata from 208Pb (1 A GeV) + p [4] are given as open symbols.

statistical uncertainties are shown.

The numbers of the kinetic energies �Ekin(Z) and �Ekin(A) of the present workare given in Tables 5 and 6, respectively.

4 Discussion

The measured residue production from the reaction 208Pb (1 A GeV) + dhas been summarised in Fig. 12 in a form of chart of the nuclides. It shows

38

Z �Ekin [MeV] Z �Ekin [MeV] Z �Ekin [MeV]

56 15.0 � 1.0 65 8.3 � 0.5 74 4.2 � 0.3

57 14.1 � 0.9 66 7.7 � 0.5 75 3.7 � 0.2

58 12.9 � 0.8 67 7.4 � 0.4 76 3.3 � 0.2

59 11.9 � 0.8 68 7.0 � 0.4 77 2.8 � 0.2

60 11.0 � 0.7 69 6.4 � 0.4 78 2.27 � 0.14

61 10.5 � 0.6 70 6.1 � 0.4 79 1.88 � 0.11

62 9.4 � 0.6 71 5.6 � 0.3 80 1.31 � 0.08

63 9.3 � 0.6 72 5.1 � 0.3 81 0.85 � 0.05

64 8.8 � 0.5 73 4.7 � 0.3 82 0.38 � 0.03

Table 5Weighted mean of the spallation-residue kinetic energies averaged over the massnumber for each element.

Fig. 12. Two-dimensional cluster plot of the isotopic production cross sections ob-tained in the present work shown as chart of the nuclides. Full black squares corre-spond to the stable isotopes. Spallation-residues and �ssion products are separatedby a minimum of cross sections at Z = (52� 4).

39

A �Ekin [MeV] A �Ekin [MeV] A �Ekin [MeV]

130 13.1 � 0.4 156 7.0 � 0.2 182 2.73 � 0.12

131 13.2 � 0.4 157 6.6 � 0.2 183 2.66 � 0.12

132 12.8 � 0.4 158 6.7 � 0.2 184 2.44 � 0.12

133 12.6 � 0.4 159 6.4 � 0.2 185 2.30 � 0.12

134 11.8 � 0.4 160 6.2 � 0.2 186 2.31 � 0.12

135 11.6 � 0.3 161 6.2 � 0.2 187 2.04 � 0.12

136 11.2 � 0.3 162 6.0 � 0.2 188 1.97 � 0.12

137 10.8 � 0.3 163 5.9 � 0.2 189 1.82 � 0.12

138 10.8 � 0.3 164 5.5 � 0.2 190 1.67 � 0.11

139 10.3 � 0.3 165 5.4 � 0.2 191 1.61 � 0.11

140 10.2 � 0.3 166 5.3 � 0.2 192 1.43 � 0.11

141 10.0 � 0.3 167 5.0 � 0.2 193 1.31 � 0.11

142 9.7 � 0.3 168 5.00 � 0.15 194 1.25 � 0.11

143 9.3 � 0.3 169 4.71 � 0.14 195 1.10 � 0.11

144 9.2 � 0.3 170 4.59 � 0.14 196 1.02 � 0.11

145 9.1 � 0.3 171 4.43 � 0.14 197 0.93 � 0.11

146 8.9 � 0.3 172 4.13 � 0.14 198 0.78 � 0.11

147 8.5 � 0.3 173 4.21 � 0.14 199 0.77 � 0.11

148 8.5 � 0.3 174 3.92 � 0.13 200 0.62 � 0.11

149 8.2 � 0.2 175 3.71 � 0.13 201 0.52 � 0.11

150 7.8 � 0.2 176 3.69 � 0.13 202 0.47 � 0.11

151 7.8 � 0.2 177 3.32 � 0.13 203 0.34 � 0.11

152 7.5 � 0.2 178 3.34 � 0.13 204 0.30 � 0.10

153 7.5 � 0.2 179 3.16 � 0.13 205 0.28 � 0.10

154 7.2 � 0.2 180 2.97 � 0.12 206 0.15 � 0.10

155 7.1 � 0.2 181 2.90 � 0.12

Table 6Weighted mean of the spallation-residue kinetic energies averaged over the atomicnumber for each mass.

40

the production of around 1000 isotopes. Fig. 12 includes also several isotopes,which are not listed in Tables 2 and 3 because of their large uncertainties, inorder to get a complete view on the production. The total reaction cross sectionin the present work for 208Pb (1 A GeV) + d amounts to �tot = (2:08�0:24) bextracted from the individual isotopes (of Tables 2 and 3). The total reactioncross section determined by summing up the nuclide cross sections from Fig.12 results as �tot = (2:28 � 0:26) b. This value agrees well with the resultof a Glauber-type calculation as described in Ref. [28] for the total nuclearinteraction cross section of 208Pb (1 A GeV) + d with realistic nuclear-densitydistributions (from Ref. [29]) that gives �tot = 2:32 b. The corresponding totalreaction cross sections obtained in Ref. [4] for the reaction 208Pb (1 A GeV)+ p were �tot = (1:87� 0:23) b from individual isotopes, �tot = (1:99� 0:27)b from summing up the total mass distribution, and �tot = 1.80 b from theGlauber-type calculation.

The increase of the total reaction cross section in the reaction 208Pb (1 AGeV) + d compared to the reaction 208Pb (1 A GeV) + p is found in a moreabundant production of medium-heavy residues (A � 120� 170) in 208Pb (1A GeV) + d reactions. This is shown in Fig. 13 where the mass distributionsof the reactions 208Pb (1 A GeV) + p,d are compared. The total �ssion crosssections of the two reactions are almost identical, while the mass distributionis slightly broader on both wings in the deuteron-induced reaction.

The element and mass distributions of the reaction 208Pb (1 A GeV) + d areshown in Fig. 13 as full symbols. The data of the present work are comparedwith the results of Ref. [4] for the reaction 208Pb (1 A GeV) + p as opensymbols. All the distributions shown in Fig. 13 have been taken by projectionon proton and mass axes in Fig. 12, and the cross sections in the overlap-ping region between �ssion products and spallation residues can thus not beobtained by summing up the individual cross sections in Tables 2 and 3.

Interesting details can be observed in Fig. 13. By comparing the mass dis-tributions of the reactions 208Pb (1 A GeV) + p,d in Fig. 13 at high masses(around A � 190� 205), it can be seen that the cross sections from the tworeactions are nearly the same. This can be understood by assuming a periph-eral collision for 208Pb (1 A GeV) + d with a hit of only one nucleon, i.e. onlythe proton or the neutron of the deuteron is interacting with the projectile,making then the reactions 208Pb (1 A GeV) + p and 208Pb (1 A GeV) + dlooking similar. Larger deviations of a few points result from missing data forsome isotopes in the proton-induced reaction. In the mass region A � 180 asmall decrease in the cross sections can be seen. This is a region of a hit of twonucleons where both the proton and the neutron of a deuteron interact withthe projectile. The result is that more mass is removed from the projectile dueto more violent collisions.

41

Fig. 13. Comparison of experimentally measured element (a) and mass (b) distribu-tions of the reactions 208Pb (1 A GeV) + d shown as full symbols (the present work)and 208Pb (1 A GeV) + p shown as open symbols from Ref. [4]. In the transitionregion between spallation residues and �ssion products, both distributions containmore isotopes than given in the corresponding Tables.

In �ssion cross sections, there are not so many di�erences to be expected be-tween the reactions 208Pb (1 A GeV) + p,d. Figs. 13 and 14 demonstrate thatthe production of the lighter and more neutron-de�cient �ssion fragments isslightly pronounced in the reaction 208Pb (1 A GeV) + d. Fig. 14 comparesisotopic cross sections of some selected elements from the reactions 208Pb (1A GeV) + d (the present work) and 208Pb (1 A GeV) + p [4]. The elements inthe upper row have been produced by �ssion. The neutron-de�cient isotopes ofthese �ssion products are produced slightly more abundantly from the 208Pb

42

Fig. 14. Comparison of the isotopic distributions of some selected elements. Produc-tion cross sections from the present work for 208Pb + d are shown as full symbolsand from Ref. [4] for 208Pb + p as open symbols. In the upper row, the produc-tion mechanism is spallation-�ssion, while the nuclei shown in the lower row areproduced by spallation-evaporation.

(1 A GeV) + d reaction, while the neutron-rich side seems to be equally popu-lated. This di�erence can be understood as an indication that the prefragmentsfrom the reaction 208Pb (1 A GeV) + d extend to higher excitation energies,and thus the evaporation chains extend to lighter and more neutron-de�cient�ssion fragments. The isotopic distributions of spallation-evaporation residuesshown in the lower row of Fig. 14 have very similar shapes. For the heavi-est elements (e.g. mercury), however, the proton-induced spallation producesslightly higher cross sections for the lightest isotopes, indicating that collisionswith protons induce higher excitation energies for a given number of protonsremoved from the lead projectile than collisions with deuterons do. The rea-son might be that collisions leading to elements slightly below the projectileare more peripheral, on the average, in deuteron-induced reactions because,otherwise, the two nucleons of the deuteron { instead of a single one { wouldhave a larger chance to interact with the lead nucleus. For the lighter ele-ments, the evaporation of protons and neutrons has come to an equilibrium,leading to an almost identical shape of the isotopic distributions around theevaporation-residue corridor [30], also introduced as the evaporation attractorline [31]. The considerably higher production cross sections for the lighter ele-ments samarium and erbium again demonstrate that higher excitation energiescan be reached in the deuteron-induced spallation reaction.

43

The mean kinetic energy of �ssion products from the reaction 208Pb (1 A GeV)+ d reaches a plateau value of about 60 MeV in the range Z = 22�46. This isabout 10 MeV lower than for the reaction 208Pb (1 A GeV) + p, see Fig. 9(b).Fig. 9(a) shows the linear dependences of the �ssion-fragment velocities. Thetwo reactions investigated show very similar trends. The fragment velocitiesfrom 208Pb (1 A GeV) + d have systematically lower values indicating loweratomic numbers of the �ssioning parent nuclei, corroborating the observedlower plateau values of the kinetic energies.

As the atomic number of the �ssioning element is, in average, smaller in 208Pb(1 A GeV) + d reactions compared to 208Pb (1 A GeV) + p, this resultsin smaller velocities and kinetic energies of the fragments due to a weakerCoulomb interaction between the two fragments. In addition, the element ofthe �ssioning nucleus is lighter in average, the distribution of the �ssioningelements is broader and extends further down in the reaction 208Pb (1 AGeV) + d. In the reaction 208Pb (1 A GeV) + p the lightest �ssioning systemwas found to be hafnium (Z=72). From the reaction 208Pb (1 A GeV) + dthe lightest �ssion fragments seem to originate from �ssioning nuclei belowytterbium (Z=70). There also seems to be a slight di�erence in the �ssioningsystem producing the heaviest fragments. In the reaction 208Pb (1 A GeV) +p they originate from the �ssion of lead isotopes (Z=82), while in the reaction208Pb (1 A GeV) + d the main contributor to the heaviest fragments seemsto be about 2 charge units below, i.e. mercury (Z=80).

The comparison of the momentum distribution of spallation-evaporation residuesbetween the reactions 208Pb (1 A GeV) + p and 208Pb (1 A GeV) + d is shownin Fig. 10(a) and (b). It can be seen that the average mean longitudinal mo-mentum and standard deviation of the distribution are essentially identical forthe two reactions. Also the mean kinetic energies of spallation residues, as afunction of proton and mass numbers (Fig. 11(a) and (b)), from the reactions208Pb (1 A GeV) + p and 208Pb (1 A GeV) + d have practically identicalbehaviour.

The average mean values agree rather well with the experimental systematicsof Morrissey in Fig. 10(a) at heavier masses. The similarities in the momentumdistributions of the two reactions and the good agreement with the system-atics corroborate the conclusion of Morrissey that the characteristics of themomentum distribution show a universal behaviour as a function of the massloss in the reaction, independently of the target-projectile combination. Onlyat lighter masses there starts to be a clear deviation from the straight-line sys-tematics of Morrissey. There already exists previous evidence for a deviationfrom the Morrissey systematics with decreasing mass number [23,32]. The dataof Fig. 10 indicate a saturation in the longitudinal momentum at small masses(A � 130� 150). The behaviour for lighter masses is not accessible, becausethere is no production of spallation-evaporation residues below A � 125 in the

44

present work. In Ref. [23] the longitudinal momentum has been measured fromthe reaction 238U (1 A GeV) + Pb for medium-mass residues (A � 100� 170)using a similar experimental set-up as in the present work. The data in Ref.[23] would indicate that the average mean longitudinal-momentum values startto increase - and eventually even to exceed the velocity of the primary beam -with decreasing mass number. A theoretical explanation for this phenomenomof accelerated light spallation-evaporation residues has been presented in Ref.[33].

5 Conclusions

The production cross sections and the kinematical properties of about 1000primary residual nuclei produced in the reaction 208Pb (1 A GeV) + d werestudied in detail for all elements from titanium to lead. The reaction productswere fully identi�ed in atomic number and in mass number, and the velocitydistribution of each individual nucleus was measured. The data of the reaction208Pb (1 A GeV) + d were extensively compared with the similar experimentof the reaction 208Pb (1 A GeV) + p.

The total spallation-�ssion cross section of the reaction 208Pb (1 A GeV) +d was measured to be slightly higher compared with that from the reaction208Pb (1 A GeV) + p. Most part of the increase of the total reaction crosssection in the deuteron-induced reaction was found in a higher spallation-evaporation residue cross section, in particular in a stronger population offragments between A = 120 and A = 170.

It was noticed that elements below ytterbium may contribute to the �ssionyield in the reaction 208Pb (1 A GeV) + d, which is, in average, four chargeunits less that in the reaction 208Pb (1 A GeV) + p where the lightest �ssioningelement was determined to be hafnium.

The kinetic energies and momentum distribution of spallation-evaporationresidues were observed to behave similarly in the reactions 208Pb (1 A GeV)+ p and 208Pb (1 A GeV) + d. For the average mean longitudinal momentuma clear deviation from the empirical systematics of Morrissey was noticed withdecreasing mass number.

The mass distribution of residues from the deuteron-induced spallation-evaporationreaction can be understood by considering that the two nucleons in the deuteronare divided by a large distance on the average. The heaviest residues are pro-duced by collisions with only one of the nucleons, while collisions with bothnucleons lead to lighter residues.

45

6 Acknowledgements

The authors are indebted to K.H. Behr, A. Br�unle and K. Burkard for theirtechnical support and assistance during the experiment, to the group of P.Chesny for building the liquid-hydrogen target, and to J. Pereira for providingcalculations for the transmission correction. This work was partially supportedby the European Union under the contract ERBCHBCT940717.

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In - GSI · Poland Abstract The pro duction cross sections and the kinematical prop erties of primary residual n uclei ha v e b een studied in the reaction 208 Pb (1 A GeV) + d. Isotopic