Compound nucleus reactions of B with Ta and Ag

L/

No&&@’ Physics

2.A.l:

2.1)

A228 (1974) 397- 414; @

Not to be reproduced

COMPOUND

by photoprint

NUCLEUS

North-HoIhd

PublisJhg Co.,

Art~sferda~n

or microfilm without written permission from the pubiisher

REACTIONS

OF B WITH Ta AND Ag

H. DELAGRANGE, F. HUBERT and A. FLEURY Cenire d’Etudes Nucl&i+es de 3~rde~l~~-~~ud~~nan, Laborer&e de fhirnie ~~~~~a~~~ERA m. 144, Le Haut Vfgneau, 33170 Gradfgmm, France Received 25 February 1974 Abstract: Excitation

functions and mean recoil ranges are reported for the formation of la*Pt, zR61r, 1850s in 1°@llB reactions with “ITa and for 113Sn in l”*‘rB reactions with 1o7-l0ogAg. The stacked foil technique was used. The results are indicative of a compound nucleus process. Mean recoit ranges are compared to theoretical calculations with corrections for multiple scattering. The agreement is satisfactory. Evaporation calcuiations were performed with a modified statistical model code GROG1 2. A good fit is obtained with parameters derived from studies of nuclei at low excitation energies; no enhancement of the rate of y-emission is needed.

E

NUCLEAR REACTIONS lslTa(‘o* rlB, X); ro7Ag(10*“‘B, X); ‘osAg(‘lB, X), Eta. = 50-104 MeV, Ezra = 50-114 MeV; measured o(E) and mean recoil range for lssPt, 1861-r,lssOs and “%n formation.

1. In~odu~t~on

The essential characteristics of compound nuclei formed by heavy ions are high excitation energy and high angular momentum. Analysis of the experimental results of reaction studies makes it possible to obtain the main parameters governing the deexcitation of the nuclei. Gamma-ray emission is not specific to reactions with high angular momentum, but it does play an important role, notably in a widening and a shift of the excitation functions toward higher energies. Gilat et al. ‘) have shown that the agreement between experimenter and calculated excitation functions depends strongly on the choice of the parameter CL which controls the probabihty of electromagnetic transitions. The values of <, required depend on the system under consideration and it seems that for some reactions, y-ray emission is enhanced considerably over the rates of emission deduced from the resonant capture of neutrons. 117this paper, we have undertaken to study the de-excitation ofcompound nuclei with angular momentum distributions midway between those typically produced by light projectiles (e.g. “He) and those produced by heavier ions (e.g. “C, etc.). We report the study of reactions induced by ‘OB and “B with tantahtm and silver targets. In sect. 2, we give the experimental details pertinent ta the measurement of the excitation functions, together with the experimental results. We discuss here only those results relevant to evaporation from a compound nucleus. The study of other reaction mechanisms will form the subject of a subsequent publication 33). In sect. 3, 397

398

H. DELAGRANGE

et ai.

we describe the range-energy relations we have used for the heavy recoil nuclei. The two subsequent sections are devoted to the theoretical study of the reactions that involve compound nuclei. 2. Experimental methods and results

We have irradiated foil stacks consisting of “thick” targets separated by aluminium collecting foils. Beams of r*B and “B of M 10.5 MeV/a.m.u. were obtained at the Yale University HILAC. The energy loss of the ions in the stack was calculated from the tables of Northcliffe and Schilling “). The integrated beam current was monitored with a Faraday cup. The identification and measurement of the products were made with a 10 cm3 germanium-lithium coaxial detector. The energy resolution of the detector system was = 5 keV. Characteristics Isotope

TABLE 1 of the observed radionucleides

Half-life

Branching ratio (x 102)

Ref.

(Ta+B) system 10.2 d 15.8 h 94 d 22.6 h 68 d

64

h

19.9 h

“%n l*lIn ‘Wd ““Ag

140 115

d d

115.2 2.83 453.2 40

d d d d

188 197 297 646 178 209 210 226 229 ‘365 59 1122 (Agi- B) system 392 173 88 280

37.6 74 81.3 32.5 4.6 28 65 74 34

64 89 32 32

The mean recoil range of each product was calculated from the fraction of activity .f found in the collector, B = f T(Q,+ ao)Poo, where T represents the target thickness and cro and err the cross sections at the exit and entrance of the beam in the target, respectively 34). We have listed in table 1 the isotopes observed together with the half-life, the energy and the branching ratio of the y-rays. Experimental cross sections and average

l*‘Ta(lo*

IlB, X)

400

TABLE 2 Experimental results

Beam energy (MeV)

l8sPt O--

18% R

0

Experimental results for (‘8’Ta+“B)

interaction

50.4&2.9 55.0+2.7 60.8k2.5 64.4-1-2.5 70.1+2.2 73.1 k2.4 78.452.1 81.Ok2.0 86.3*2.1 88.6h2.0 94.112.0 95.9k2.0 100.9fl.8 102.5hl.8 107.111.7 109.1+1.6 110.7kl.7 112.211.7 113.5&1.6

59.3+ 0.3 333 i 7 429 &IO 382 & 8 147 & 3 84 & 9 27 * 1 15 + 1

0.23 10.01 0.48 ho.01 0.49&0.03 0.57hO.03 0.45+0.08 0.60&0.04 0.63+0.04

21 267

16 =

9

325 i 6 336 5 8 173 &17 138 i 6 88 *I4 62 A- 4 52 ; 9 22 5 2

12 16.3& 0.3 8 k-2

G

R

16.1+ 0.3 $11 64 i 9 64 i 1 64 I 1 95 i 2 176 I_ 5 399 510 640 +20 849 _c 7 981 &8 869 i-19 851 I_ 2 587 &16 498 i 7 417 & 6 376 t 6 325 & 7 49

Experimental results for (lslTa+loB) 49.4k3.0 59.Ok2.5 67.6*2.3 75.3 k2.0 84.8i2.0 90.0*1.9 96.2hl.7 102.2h1.6

l85OS

-R

0.56*0.05 0.65 *0.06 0.73 hO.03 0.78f0.10 0.7910.10 0.96&0.09 0.9 *0.2

& 3

0.44 fO.04 0.46 0.42 0.36 0.39 0.58 0.68 0.68 0.74 0.71 0.79 0.79

&0.02 kO.03 &to.02 io.02 &to.02 10.04 50.02 10.02 io.03 io.04 _CO.O6

1.04 ;0.04 0.79 50.08

interaction

0.31*0.04 0.51 io.13

5.7& 0.3 247 J- 6 375 117 206 & 8 80 i 3 42 i_ 2 16 ” 1

0.30f0.07 0.50&0.05 0.44*0.04 0.7510.10 0.82*0.13

22 427 1055 1051 615 308 153

i & ill & i-7 I t

2 2 7 4 1

0.468 0.49 0.58 0.60 0.58 0.64

ho.004 Iko.03 10.01 10.02 10.02 $0.04

Experimental results for “%I Beam energy

Ag+“B

(MeV)

G

41.7i2.6 42.0&2 50.3 +2 50.5+2.3 56.7&2.1 58.1&2 65.1f1.9 77.0+ 1.7 77.411.7 82.1&1.7 88.8kl.5 94.551.6 100.811.4 102.0*1.4 106.5+1.5 113.0*1.6

45 0.2 61 0.6 43j, 1 32* 3 925 2 135+ 2 322% 5 583kl7 593 &22 529& 12 450% 8 392* 4 3991 2 399&10 393& 2 350* 3

+ l13Sn R

Beam energy --

0.62&0.01 0.70*0.03 0.72+0.01 0.7610.03 0.93 *to.04 1.08&0.07 1.05+0.01 1.10~0.04 1.07~0.01 1.23+0.02 1.26f0.05 1.24f0.02 1.27&0.03

WeV) 31.8Oh3.40 47.95+2.55 49.20f2.60 55.95+2.55 63.00&2 68.90fl.90 75.05f1.85 75.65+ 1.85 81.5Ohl.80 85.80*1.80 91.8Okl.60 91.90fl.60 97.00 + 1.60

Ag+l”B CT 7* 0.3 93Cl6 1165 2 412& 4 398C 3 356+ 5 314+ 3 268& 3 317% 3 411* 4 368112 327% 5 268& 5

+ “%n R

0.50+0.04 0.56hO.03 0.75+0.03 0.8OiO.02 0.81 f0.03 0.76f0.05 0.92kO.04 0.9510.03 1.0310.02 1.06+0.05

“‘Ta(“‘.

“B,

X)

401

TABLE 2 (continued) Beam energy (MeW 41.30+2.10 56.40+2.00 62.7Oh1.70 69.6Ok1.60 80.4551.45 86.90& 1.40 97.25i1.35

_

109Ag+‘0B + l13Sn o

9+0.4 71&l 66&l 105&l 58954 674&4 609&9

R

0.51*0.04 0.5450.06 0.5910.06 0.92L-tO.05 0.95kO.04 1.10*0.05

Beam energ>

losAgf’lB

(MeV)

(T

48.7A2.3 58.3+1.9 63.9C1.9 70.2h1.8 71.3&1.6 76.2kl.7 83.3k1.6 87.8h1.7 94.951.3 100.6& 1.4 106.6+ 1.3

351 3 203& 6 2461 6 227* 16 246& 1 190% 2 174& 4 2101 0.4 4481 5 5s9*10 757*13

+ “%n

R 0.91iO.12 0.71 f0.06 0.6510.02 0.65iO.01 0.71 _cO.Ol 0.78&0.03 0.88&0.01 1.21+0.03 1.30+0.02 1.30t0.05

Cross sections (0) are given in mb and average recoil ranges along the beam axis (R) in mg/cm’. The errors which are quoted in the table result from the statistical uncertainties in the activit) measurements.

recoil ranges are presented in table 2. Cross sections (G) are given in mb and average recoil ranges along the beam axis (R) in mg/cm’. The errors which are quoted in the table result from the statistical uncertainties in the activity measurements. We used targets of natural silver and also targets of the separated ‘09Ag. The excitation functions were then constructed by difference measurements. The experimental results can be classified by observations of the shapes of the excitation functions and the variation of the mean ranges with the energy of the incident ions. Figs. 1, 2 clearly show the qualitative characteristics of reactions corresponding to the symmetric evaporation from a compound nucleus. The excitation functions pass through a maximum and the mean ranges increase with the energy of the incident ions. 3. Mean ranges of recoil nuclei The measurement of the mean ranges of a recoil nucleus provides a criterion for the compound nucleus formation. If there is total transfer of momentum from the incident ion to the target nucleus, the product formed will recoil with an average kinetic energy E, given by the relation:

ER= E,(A, A,)/(& + A,)‘where Eb represents the energy of the incident ions, and A,, A, and A, the masses of the product, of the incident ion and of the target, respectively. We have assumed total momentum transfer and have calculated the mean range by the formalism developped by Lindhard et al. 16) and modified by Blaugrund 17). A test of the assumption is provided by comparison of the measurements with the calculations.

402

H. DELAGRANGE

3.1. CALCULATION

OF RANGE-ENERGY

et al.

CURVES

Lindhard et al. divide the stopping power (dE/dR) into the sum of an electronic contribution and a nuclear contribution. The nuclear stopping power is calculated from elastic scattering of the ion by an atom. A screened Coulomb potential of the Thomas-Fermi model is used. For velocities less than (e2/h)Zf, the electronic stopping power expressed in terms of reduced variables is given by (deldp), = kc”, with

where A and Z represent the mass number and the charge of the nuclei. The signs 1 and 2 characterize the moving ion and the absorber atom respectively. The constant k varies only very slowly with Z, and Zz (generally between 0.1 and 0.2). It has been observed that experimental values of k may differ from eq. (1) by as much as 3. Thus we will fix k by comparison to experiment. By expressing the energy E and the range R in terms of the reduced variables E and p, Lindhard et al. obtain universal curves independent of the stopping medium, and of the moving ion. Various analytic forms of the nuclear stopping power have been given I**’ “) making it possible to fit the values given by Lindhard et al. In our calculations, we have used the following form I*): (de/dp), = -0.2 log (&ei.215)+2

x 10-3/~o*815 .

This function is in accordance, within 2 “/,, with the curve given by Lindhard for an energy domain: 2 x 10e3 < E < 10. 3.2. AVERAGE

RECOH. RANGES

PROJECTED

ON THE BEAM DIRECTION

The range R calculated with the help of the relation R = jds/(de/dp) represents the total recoil distance of the nucleus. This distance differs from the range in the beam direction R,, because of the multiple scattering. It is the value R, which is directly obtainable by experiment, and therefore we must calculate R, from R. Let Q,be the average scattering angle in the laboratory system due to collisions. The projected range is given by the following relation: R, =

sdc:

(cos CD)_

Wdp

By adapting the formulas of multiple scattering of the electrons in the case of heavy ions, Blaugrund “) obtained an expression for the mean value (cos @). Here we shall simply recall the formula, (cos @> = exp ~-(G(~)/2~)~~,

ls’Ta(‘o*l’B,

with 1 =

s

?!i!.!&

E

X)

&,

I’

Al/A,

=

E(d&k’)

where se and E represent respectively the energy given interval. The term G(r) is defined

I

1++--+2+*

G(r) =

403

f

<+A!

at the beginning

I

forr<

(-l/r)n-i

n=3

1

(2n + 1)(211- 1)(2n - 3)

_g f r

and the end of a

(-I’)”

_____

n=3

2

forr

> 1.

(2n+1)(2n-1)(2n-3)

The smaller the value of r, and the smaller the energy the greater the ratio R,/R. As an example, we show in table 3 the values of (R-R&R that one obtains for different systems. In this study A,/A, z 1 and therefore the correction for scattering is very important. TABLE 3 Nuclear

scattering

System

14N

40Ar in B

with LSS-Blaugrund r = Al/Al

5.8 73.0

0.07

2.3 6.9

27A1

2.8 10

theory R-R,,

56 21

4

8 5

5.26

5 3

*03At in lg8Au

0.8 3.03

1.08

32 25

lssOs

in lslTa

1 4

1.02

33 25

“%n

in Io9Ag

1.3 13

1.04

30 16

34CI in

3.3.

calculated

Dimensionless energy F

in 19*Au

14*Sm in

correction

INFLUENCE

*‘Al

OF

PARTICLE

150

EMISSION

1.2

ON

THE

5

RANGE

The nucleus formed in the primary interaction acquires a certain momentum and then moves with a velocity I/. The evaporation of particles then communicates a velocity V’ to this nucleus in the c.m. system. The range of the recoiling nucleus will thus be determined by the resulting velocity V’ = I/+ V’. The expression giving the mean value of the projected range on the direction of the initial velocity, namely

H. DELAGRANGE

404

et al.

(R,), shows 20-22) that the variation of (R,) with V’ is slight if ( V2)/V2 is small. Also (R,) depends very little on the anisotropy of the emitted particles. When the interaction leads to total momentum transfer, the value of the ratio
(VZ) = 8Tn/(A,+A,+A& where T, represents the average total kinetic energy of the emitted neutrons and A, the mass of the recoil nucleus. The value of T, can be deduced from experimental

3

4

5 Recoil

6 Energ

(MW)

Fig. 3. Range-energy curves for IsaPt, ls61r, 1 s50s recoils in ‘sITa and l13Sn recoils in Ag. The dashed curve is the theoretical expectation as calculated with the theory of Lindhard et al. and corrected for the multiple scattering by Blaugrund. The solid curve gives the best fit among the experimental points.

excitation functions. For example, it is around 15 MeV for the reactions “iTa (“B, 6n)185Pt. One then obtains for these reactions ( V’2)/V2 M 0.01. Thus the deexcitation of the compound nucleus by neutron emission barely affects the range of the recoil nuclei. In the case where the compound nucleus emits an cl-particle of energy E,, the velocity will be given by V” = 8 EJA:. If E, is z 20 MeV one then

obtains ( V2>/ V2 z 0.09. The range of the recoil nucleus thus will be increased by approximately 5 %. In conclusion, these examples show that the average projected range is essentialIy a function of the primary momentum transferred in the reaction, and that the modifications due to the evaporation of particles are very small. 3.4. COMPARISON

WITH

EXPERIMENT

In figs. 1 and 2 we show the experimental values of the cross sections and the mean ranges. The qualitative behavior is exactly that expected for “complete fusion”, or compound nucleus reactions. In fig. 3 the experimental range values are compared to the theory of stopping. We conclude that the calculated range-energy curves give an accurate representation of the observed ranges. We will use these range-energy curves in the accompanying paper to describe the expected behavior of transfer reactions. 4. Calculation of the excitation functions The first requirement for a statistical model calculation is the estimation of angular momentum J in the compound nucleus. The ~-distribution of the tota inelastic cross section rr,(E, .7) can be calculated as follows:

In the expression, P% is the reduced de Broglie wavelength for the projectile in the c.m. system, Sis the channel spin, s and Iare the spin of the incident particle and of the target respectively; T*(E) are the transmission coeflieients for the incident particle of orbital angular momentum 1. We have calculated these toe ients for the systems (Ta+B) and (AgfB) with the parabolic potential approximation ‘“), To calculate cCN, we used the empirical expression for ae,/cr, as a fuu~tio~ of EC&V presented by Alexander and Lanzafame “) (EC.,. is the bombarding energy in the c-m. system and Vis the classical Coulomb barrier energy). We then make the final assumption that cross section lost to transfer reactions is from the high angular momentum part of the population distribution. The second step of the calculation has been performed with a program derived from that of Grover and Gilat 26). This program makes it possible to follow the deexcitation of the nuclei by emission of neutrons, protons, a-particles and photons. - From an initial distribution of excited nuclei p P,(E, J), the program calculates the probabilities of emission ofeach particle and the distribution of residual nuclei. Since the y-emission can leave the nucleus with sufficient energy to permit the subsequent emission of particles, the population distribution obtained following y-emission is added to the initial distribution. This method of calculation thus makes it possible to take into account explicity the y-emission. The calculation is repeated for each

H. DELAGRANGE

406

et al.

value of E and 9. The population distribution of the residual nucleus (p + 1) Ph+ 1 - (E, J) is then used as point of departure for the following step. The input data necessary for the program are the following: The transmission coeficients of the emitted particles. We used the optical model calculations of Mani et al. 27 ) for the neutrons and protons, and of Huizenga and Igo 28) for the a-particles. The normalization factor, tL allows adjustement of rates of TABLE 4

Level density parameters used in the calculation

J,f&z

A

A

(MeV-‘)

(Mek’)

21.05 21.94 22.00 21.95 21.87

191 190 189 188

21.62 22.50 22.56 22.51

187 186 185 184 183

21.96 21.88 22.00 22.11 22.53

J.,,IJ,,,id

Te isotopes

Pt isotopes 192 191 190 189 188

J,,tl@ (MeV-I)

64.31 73.61 68.09 75.29 73.59

0.73 0.84 0.79 0.88 0.87

120 119 118 117 116

16.03 16.18 16.12 15.87 15.58

0.80 0.92 0.87 0.96

119 118 117 116

15.03 15.19 15.13 14.90

1.00 0.99 1.02 1.00 1.15

116 115 114 113 112

14.27 14.04 13.76 13.46 13.11

Ir isotopes

55.78 65.53 58.35 64.35 57.18

1.39 1.65 1.49 1.67 1.50

48.10 54.76 50.99 54.76

1.21 1.40 1.32 1.44

41.88 47.46 39.56 41.86 36.44

1.10 1.27 1.07 1.15 1.02

Sb isotopes

69.62 79.54 74.56 81.15 OS isotopes

Sn isotopes

84.99 82.38 84.7 81.92 93.27

y-emission. It depends on the nuclei studied and on the multipolarity of the y-radiation. The experimental sources of dipole y-emission widths are neutron capture reactions 2g). These are the widths we have used. For quadrupole y-emissions one has few experimental results. We have arbitrarily taken a value of IO3 for the ratio of the dipole to quadrupole y-width. The level densities. The formula of level densities used is that proposed by Lang 30). In this treatment, the state densities o(E, M) for an energy E and a value A4 of the projection of angular momentum is given by the relation w(E, M) = w(E -M2h2/2S, w(E, 0) = B- 1 exp (2JaE)/(E

0), + 3/2t)“,

where 3 represents the moment of inertia of the nucleus and a the usual level-density parameter, while B is a constant which has a value B = 12(2 Y/h”)*. The thermodynamic temperature t is linked to the excitation energy by the relation E=at’ - 3/2t.

181Ta(10*11B,

X)

407

The Lang formula diverges when t tends towards 0. One then uses a constant temperature t, fixed at 0.2 MeV. The level density Q(E, J) is obtained as the difference between the densities o(E, M = J) and o(E, M = J+ 1). Here E represents the effective excitation energy, i.e. total excitation energy reduced by the pairing corrections 6. We have used the values of 6 tabulated by Gilbert and Cameron 31). The yrast energies imposed by Lang’s prescription are Ej = (J-t-4)%2/24+6. The parameters which remain to be defined for the calculation of the densities are a and I, the moment of inertia. The level-density parameter a is calculated with the help of the formula given by Gilbert and Cameron 31) a/A = 0.120+0.00917

S,

S being the shell correction and A the mass number of the isotope. The moments of inertia 9 were deduced from the yrast energies. These last were numerically calculated for each nucleus by the shell model code Yrastgh of Grover et al. Then a least squares fit of the parabola E.

=

J

(J+S-)2h2 +a

24

to the numerical yrast energies gives the effective moment of inertia 3. A list of the parameters used is given in table 4. The serf and frigid represent respectively the effective moment of inertia and the moment of inertia calculated by assimilating the nucleus to a rigid sphere. One may note that the effective moment of inertia is lower than frigid for the greater part of the nuclei Pt, It-, OS. On the other hand, for the Te, Sb, Sn nuclei, it is higher.

5. Results 5.1. CHARACTERISTICS

OF THE

THEORETICAL

ANALYSIS

The de-excitation of a nucleus, at given energy and angular momentum, is determined by the relative values of the probabilities of emission of particles and y-rays. The competition between the various paths of de-excitation depends on the characteristics of the various nuclei involved. We have calculated for several nuclei the probabilities of emission of neutrons, protons, alphas and y-rays. i.e. k,, k,, k, and k,. The results obtained are presented in the E, J de-excitation plane in figs. 4-6. In these figures, the dotted line represents the yrast levels. The solid lines define the set of points of equal emission probability. Let us examine, for example, the various possibilities of emission of the “‘Pt and ’ 13Te nuclei, two nuclei for which the shell effects are very different. In the case of the IsaPt, fig. 4 shows that the emission of neutrons is the most probable path of de-excitation for the region of the (E, J) plane

et al.

H. ~~LAGRA~GE

408

w

40 Fig.

%I

80

JIM

20

do

60

4. Emission probabilities for ’ 8Vt nuclei.

Fig. 5

Fig. 5. Emission probabilities

for af Te nuclei.

lslTa(‘o*‘lB,

-

Fig. 6. Contour

plot of populations

X)

409

Rpulotimin

in ‘92*19’*‘90*‘89Pt

for 85 MeV “B

bombardment

of ‘8’Ta.

TABLE 5 Values of the effective moment of inertia for ‘13Te and ls8Pt excitation products Parent

Daughter

nucleus

’ “Te *“Sb *09Sn

’ s’Pt 18’Ir ’ 840s

reached

by our experiments

(i.e.

up to

nucleus

(n-emission) (p-emission) (a-emission) (n-emission) (p-emission) (n-emission)

nuclei

and

their

daughter

de-

4,,,lfi-2 (MeV)-’ 54 47 45 30 74 75 80 82

90 MeV and 50 h); k, is between 93 “/, and 98 y0 for all excitation energies above z 19 MeV. The emission of protons and Xparticles is considerably less for this region of the (E, J) excitation plane. Moreover, one notes that the curves of equal probability are only very slightly dependent on the value of J in this domain. When the excitation energy decreases, however, neutron emission comes into close competition with photons. Fig. 4 shows that more than 50 % of the l**Pt nuclei become de-excited by y-emission in a region situated between the yrast line and the line noted 50 % (the y-cascade band). For the low values of J, this band is situated

410

H. DELAGRANGE

ef al.

= B,, above the yrast energies (B, is the binding energy of the neutron in the 188Pt nucleus). For high J the y-cascade band narrows and finally disappears for a value of y-emission have similar behavior; ofJ M 50 h. Different lines of equal probability they terminate on the yrast line in a relatively narrow domain of angular momentum. This is the “pinch-off” effect 35), resulting from the high probability of cc-emission for high values of J near the yrast line. The li3Te nucleus presents quite different characteristics from those we have just set out. Thus for the values of J less than approximately 30 h one notes that it is the emission of protons and to a lesser extent of m-particles which is preponderant (fig. 5). This result is explained by noting that for the li3Te nucleus the binding energy of the neutron has a value twice that of the proton (B, = 8.74 MeV, B, = 4.12 MeV). As for the a-particle, its binding energy is negative (B, = ,--2.59 MeV). Thus despite the Coulomb barrier, these charged particles are favored even when the excitation energy of the nucleus is close to B,. Another notable aspect of the de-excitation of the ‘13Te nucleus is the suppression of the “pinch off” effect. The cc-n-y competition for high values of the angular momentum is linked to the characteristics of the nuclei concerned, notably to the effective moment of inertia. Table 5 compares the values of this parameter for the parent nuclei ‘13Te, 188Pt, and those resulting from the emission n, p, CLThe a-emission from ’ 13Te leads to lo9Sn for which the value of Yen is very low. We thus obtain yrast energies of lo9Sn, much higher than those for li3Te, and level densities that are much lower. Therefore for high values of J, cc-emission cannot be competitive with the y-emission. On the other hand, for the 188Pt nucleus, the values of Yen favor a-emission. It is thus possible to foresee the characteristics of the de-excitation chains with the help of these diagrams. The (Ta+ B) interactions lead to a domain of the (E, J) plane for which the de-excitation takes place essentially by neutron emission. The reactions of the type 18’Ta( lo, “B , xn)Pt will therefore present the highest cross sections. On the other hand, in the case of the (Ag+B) interactions, de-excitation chains involving the emission of charged particles will become competitive. In fig. 6, we present an example of population distributions of excited nuclei 192,191*190z189Pt formed in the (Ta+l’B) interaction at 85 MeV. In this figure, the dots indicate the maximum value of the distributions. The lines represent the points of equal population. The initial compound nucleus is characterised by a single value of excitation energy and a distribution in angular momentum limited by Jcri,. The emission of a neutron leads to the 191Pt nucleus for which the distribution in E is very wide whilst the values of J are barely modified. The same is true for the subsequent nuclei. The emission of y-rays is competitive with that of neutrons only at the end of the evaporation chain. Part of the energy is carried away by y-rays. This shifts the excitation functions toward higher energies, The parameters capable of modifying the region of y-emission (k, >= 50 %), and therefore the position and the form of the excitation functions, are essentially the normalization constant for the rate of y-

‘s’Ta‘a(‘o*llB,

X)

411

I 5 3

s

e 0

10‘ 7 5 3

lo“

I

I

I

I

70

50

I

I

90 Beam

Energy (NV)

Fig. 8. Experimental and calculated results for the reactions ‘*‘Ta((“‘B, .5n)+(“B, p4n))ls61r and ls’Ta((LoB, 6n)+(“B, p5n))‘850s. The notation is identical to that of fig. 7.

Fig. 7. Experimental and calculated results for the reactions ‘81Ta(“B, 4n)t8.*Pt and I*lTa((“B, 6n)S-(“B, p5n))‘s61r. Product cross section o relative to compound nucleus reaction cross section dcN are plotted as a function of beam energy. Parameters used in the calculation are those selected a priori.

lo+-

I 40

I

I 60

I

I Bean

Fig. 9. Experimental (“‘B, 2p2n))“aSn,

and calculated “‘Ag((rlB, Sn)+ 7 (log, 2p4n))“%n.

I

80

I 100

Energl

( MN)

results for the reactions 107Ag((‘oB, 4n)+(“B, p3n)-; 6n)S-(“B, p5n) (‘IB, p4n)+ (‘IB, 2p3n)) 1’3Sn, “‘Ag((“‘B, The notation is identical to that of fig. 7.

412

et al.

H. DELAGRANGE

Bern Energy 1 M IV )

Fig. 10. Calculated ,results for the reactions r8’Ta(“‘B, 5n)l*ePt and rslTa(roB, 6t1)‘*~Pt. The solid curves are the theoretical ones calculated with a truncated J-distribution. The dashed curves are the theoretical ones calculated with a non-truncated J-distribution.

Fig. 11. Calculated results for the reactions r*rTa(r”B, 5n)‘e6Pt and r8rTa(roB, 6n)ts5Pt. The solid curves are the theoretical ones identical to that of fig. 10. The dashed curves are the theoretical ones calculated with a moment of inertia X’ = 1.5 4.

1 .

1

qmmltol curw, lhmdicol curws

----3 -

I 50

I

I 70

I 90 BmEmq

(t&V)

Fig. 12. Experimental and calculated results for the reactions “‘Ta((“B, Sn)+(“B, p4n))rs61r and l*‘Ta((loB, 6n) + (rOB, p5n))ts50s. Parameters used in the calculation are those selected apriori with the exception of EL which have been decreased by a factor of 5.

18’Ta(

lo* “B, X)

413

emission, &, and the moment of inertia of the nucleus. An increase in SyLbrings about a widening of the y-cascade band. Furthermore, the greater the moment of inertia the more the yrast line will be shifted towards the lower energies for a given value of J. The effects of a variation of tL and of X, however, are all the more noticeable for a higher value of J, and thus the higher the energy of the incident ions the greater is the shift of the excitation functions. One can thus see that the comparison between theory and experiment for the excitation functions is an important test for the values of tL, if one presumes that the moments of inertia of the nuclei are known. 5.2. COMPARISON

WITH THE EXPERIMENTAL

EXCITATION

FUNCTIONS

Figs. 7 to 9 show the comparison between the experimental excitation functions (solid curves) and the calculated excitation functions (dotted curves) with parameters chosen a priori. Because of the feeding by decay ‘i3Te “2 ‘i3Sb “s “3Sn, the calculated cross sections we have presented are the sum of those of the reactions of direct formation of these three isotopes. AS shown in fig. 5 much of the cross section of Sn comes from Te and Sb as well as Sn. In the case of the (Agf B) and (Ta+ “B) reactions, the calculations are satisfactory. They well reproduce the position of the peak in the excitation function. On the other hand, for the (Ta + ‘“B) reaction, the agreement is not good and calculated excitation functions are toward high energy. Let us examine the effect of changing the different parameters. 5.2.1. Compound nucleus angular momentum distribution. We limited the J-distribution at a critical value JErit which is not very well defined. But in the reactions here, Jcrit is not too far from the maximum value of the J-distribution J,,,. So the effect of the variation of Jcrit is not too sensitive. Fig. 10 shows this effect. The solid curves are the theoretical ones calculated with a truncated J-distribution. The dashed curves are the theoretical ones calculated with a non-truncated J-distribution. It can be seen on the figure that this effect is fairly insensitive. of 4 is to shift the excita5.2.2. Moment of inertia 3. The effect of an enhancement tion functions toward lower energies as one can see on fig. 11. In this figure the dashed curves are the theoretical ones calculated with a moment of inertia 9’ = 1.54. Nevertheless the improvement of the fit is not quite good. 5.2.3. Gamma normalization j&or &_ . A decrease of &_ results in a shift of the excitation function to lower energies. For the (Ta+ i”B) reaction, the best agreement was obtained by reducing the y-widths by a factor of 5 compared to the initial values (other parameters unchanged) (fig. 12). Thus, the values of cr. used are close to those obtained from the y-widths of the capture reactions of slow neutrons. One must note that, in reactions 140Ce(‘60, xn) 144Nd(12C, xn)156-“Dy, 136Ba(20Ne, ,yn)156-XDy studied by the group ’ =-“DY, at Stony Brook ‘) the agreement depended on increasing the y-emission rate by a

414

H. DELAGRANGE

et al.

factor of 100 compared to tL deduced from low energy measurements. On the other hand, for the system ( “ITa + 4He) such an increase was not necessary. The boron reactions behave similar to those of cc-particules with the same target. In the reactions of heavy ions with rare earths the critical angular momenta are greater than for the (Ta+B) system and the population distribution of the excited nuclei of high J close to the yrast line is thus greater. It seems that in these cases the y-transitions are accelerated. Such a result is not observed here but as the J-values are lower it is not easy to see the effect. The authors are particularly grateful to J. M. Alexander for careful and critical reading of the manuscript and to J. Gilat for his kind comments on his program. They are very much indebted to B. Jones who made irradiations at the HILAC possible. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35)

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