Measurement of excitation functions and mean projected recoil ranges of nuclei in α-induced reactions on F, Al, V, Co and Re nuclei

PRAMANA © Printed in India Vol. 40, No. 3,

__ journal of March 1993

physics pp. 227-251

Measurement of excitation functions and mean projected recoil ranges of nuclei in a-induced reactions on F, Al, V, Co and Re nuclei

M ISMAIL

Variable Energy Cyclotron Centre, 1/AF, Bidhan Nagar, Calcutta 700064, India MS received 26 September 1991; revised 19 May 1992

Abstract. Excitation function and mean projected recoil ranges of nuclei produced in the

~t-particle induced reactions on F, AI, V, Co and Re targets were measured by conventional thick target thick recoil catcher technique for bombarding energies E, ~< 65 MeV. The measured cross-sections are compared with calculations considering equilibrium as well as pre-equilibrium reaction mechanism according to the hybrid and geometry dependent hybrid (GDH) model of Blann using the code Alice/85/300. High energy part of the excitation functions are dominated by pre-equilibrium reaction mechanism whereas the low energy parts are dominated by evaporation with its characteristic peak. In this paper emphasis will be placed on the GDH model, for it provides a potentially better description of the physical process i.e., a higher probability of peripheral collisions to undergo precompound decay than for central collisions. Geometry dependent model with initial exciton number no = 4 (nn = 2, np = 2, n, = 0) gives better fits compared to hybrid model with same initial exciton configuration and

mfp

parameter k = 1"0 for ~t-induced reactions on F, V, Co and Re. Whereas for or-induced reaction on A1 comparatively large initial exciton configurations (8/4/4/0) or (10/5/5/0) were required to fit the excitation functions reasonably well. Recoil ranges were converted into recoil momentum and vice versa using Lindhard, Scharff and Schiott (LSS) and Blaugrund theories.

These theories were also used to calculate projected recoil ranges for full momentum transfer pertaining to fusion reactions. The momentum transfer information was used to get clues about some aspect of the interaction from the trends and magnitudes of the observed ranges.

Keywords. or-induced reaction on F, A1, V, Co and Re; stacked foil technique; isotope production; equilibrium and pre-equilibrium decay; overlaid Alice code.

PACS No. 25"60 I. Introduction

Nuclear reactions induced by medium energy projectiles ( = 10-50 MeV/nucleon) are interesting in view of pre-equilibrium and equilibrium de-excitation processes. The highly excited ( ~ 40-200 MeV) nuclear system, produced by the projectile bom- bardment decays first by emitting a number of fast nucleons at the pre-equilibrium stage and later on by evaporating low energy nucleons (mostly neutrons in medium and heavy nuclei) at the equilibrium stage. The pre-equilibrium process has been investigated by several workers [1-7]. Excitation functions for equilibrium and pre-equilibrium reactions have been studied in (ct,

xn)

(~,pxn)

Theoretical calculations for pre-equiiibrium process have been carried out in terms of exciton-models [5-]. Several models [1-7, 13] have been proposed to explain the emission of energetic light particles by the equilibration process from the nuclear 227

M lsmail

system excited at medium energies. Predictions from these models as to excitation functions and the energy spectra of the emitted particles compared well with the existing experimental data. This has prompted a continued interest in these models as tools both to predict cross-sections for a number of practical purposes and to test the adequacy of the underlying physics. In this paper emphasis is placed on the G D H model for it provides a potentially better description of the physical process i.e. a higher probability of peripheral collisions to undergo precompound decay than for the central collision.

This work also reports the measurements of the recoil ranges of nuclei produced for getting experimental information about the momentum transfer associated with specific final nuclei. The linear momentum transfer characteristics of reactions supplements the energy partitioning characteristics of the reactions. The aim was to seek clues about some aspects of the interaction from the trends and magnitudes of the observed ranges. During the last few years considerable effort has been devoted to studies of the linear momentum transfer in light and heavy-ion induced reactions [14]. The average linear momentum transfer characterizes the global features of the projectile-target interaction and provides a convenient indication of the reaction mechanism, it will be greatest for complete fusion reactions and reduced for direct, pre-equilibrium and break-up processes in which much of the incident momentum is carried away by the fast particles in the early stages of the reaction. Several techniques have been devised to measure the momentum of the recoil nuclei. In the present work the linear momentum transfer characteristic in the ~t-induced reactions on 59Co and 5tV, were obtained employing the classical method of thick-target thick-catcher recoil range measurements [15-17]. The present work on alpha induced reactions on the target nuclei F, AI, V, Co and Re is intended to supply some new data in the alpha energy range from threshold to 65"0 MeV.

This paper is subsequent to a series of reports on gross features of the interactions of intermediate energy light projectile with medium mass nuclei [9-11]. The experiments have been performed at the Variable Energy Cyclotron Centre, Calcutta.

In this paper several excitation functions for the a-induced reactions on F, AI, V, Co and Re measured by using the stacked foil technique are being presented. The excitation functions of the radioactive products observed in reactions contain some information about the mechanism of the interaction of ~t-particles with F, AI, V, Co and Re nuclei and we were able to decipher some features of the partitioning of the incident energy into that carried away by outgoing fast particles (in contrast to evaporation), and that left as nuclear excitation. In this work calculations in the framework of the equilibrium statistical model and pre-equilibrium model were performed and the results are compared with experimental excitation functions.

Various reaction mechanisms, supported by recoil range measurements, are indicated as contributing to the production of the radioactive nuclei. The total equilibrium and pre-equilibrium cross-sections and the variation of the fraction of pre-equilibrium emission predicted by the hybrid and G D H model by using the code Alice/85/300 are presented as a function of energy.

2. Experimental procedure

Experimental methods and apparatus used in the present experiment are similar in many respects with those described in our previous papers [9-11]. We refer readers to these publications for details not described here. For flourine, the evaporated CaF 2 228 Pramana - J. Phys., Vol. 40, No. 3, March 1993

Measurement of excitation functions and mean projected recoil ranges on AI backings were used. A thin 4"34/~m aluminium foils were kept over the target for the protection of the material. In the flourine target stack there were about 12 to 15 targets. For aluminium no separate irradiation was performed. The cross-section for aluminium was obtained from the backings of gallium and antimony targets [11].

For vanadium and cobalt irradiations 50/~m thick and for rhenium 25/zm, self- supporting foils commercially available were used. A 23.4/~m thick aluminium catcher was interspersed between the two target foils. In the cobalt stack there were about six target-catcher combination and for vanadium stack about ten target-catcher combination were used. The stacks were exposed to the unanalysed external beam from the 224 cm variable energy cyclotron in Calcutta. The stacks were irradiated in a special chamber I-9-11] kept in high intensity'irradiation area. The beam spot O n the target was limited to 5 m m in diameter by using 10.0cms long AI collimator in front of the target stacks. The beam current on the targets was kept below 200 nA.

The total ~t-particle beam was collected and measured using a calibrated O R T E C current integrator. Additionally total beam current was also monitored through the production of 22Na and 24Na in target backings and catchers [18]. The mean beam energy in each foil of a stacked foil assembly was calculated from energy degradation of the initial beam energy using the coefficients obtained from fitting the stopping power data for different materials. The stopping power tables of Williamson et al [19] were used for fitting. The fitting procedure is explained in detail in [9-11]. The unanalyzed beam energy resolution was ~ 0-2 MeV and accuracy in absolute energy is expected to be - 2"0 MeV. However for the excitation functions the energies were

Table I. Half-lives, 3,-energies, branching ratios of the ~-decays and Q-values for

~t-induced reactions on F, AI and Co.

Half- Er I s Q-values

Nuclide lives (keV) (abs) Reaction (keV)

22Na 2.602y 1275.0 0"999 19F(ct, n)22Na - 1949.3 511-0 1'000

24Na 14"96h 1368.6 1"0 27A1(~, 4p3n)24Na - 59722-6 27Al(ct, ct2pn)24Na - 31426-7 22Na 2'602y 1275"5 0"999 27Al(~t,4p5n)2ZNa - 79100-3 27Al(~,,t2p3n)22Na - 50804-4 27Al(ct, 2ctn)22Na - 22508-5 27Al(ct, 9Be)22Na - 20935"0 6°Co 5"272y l 173.0 1.000 59Co(ct, 2pn)6°Co - 20803"9

1332-0 1-000

SaCo 70"76d 8 1 0 " 8 0 0 " 9 9 4 59Co(ct, 2p3n)SSCo - 38749"4 59Co(~, ~n)58Co - 10453"6 57Co 217"7d 122"10 0 " 8 5 6 SgCo(ct, 2p4n)STCo -47322"6

59Co(ct, ct2n)57Co - 19026"7

~6Co 78"76d 8 4 6 " 8 0 0 - 9 9 9 S9Co(ct,2p5n)56Co - 58698"5

~9Co(~t, ct3n)S6Co - 30402'6 5'tMn 312-2d 835-00 1 - 0 0 0 SgCo(~t,4p5n)54Mn - 73760-5

~gCo(ct, ct2p3n)S4Mn -45464'7 59Co(ct, 2~tn)S4Mn - 17168'8 59Co(at, 9Be)54Mn - 15595"3 h = hour d = days y = year

Pramana - J. Phys., Vol. 40, No. 3, March 1993 229

M Ismail

recalibrated with respect to Q-values of lSSRe(~t,4n)lSSIr and 51V(~t,3n)52Mn reactions which are - 33.376 MeV and - 23"286 MeV respectively.

The production cross-sections were determined using the absolute yields of charac- teristic ?-rays belonging to each final nucleus. The ?-rays emitted by the irradiated targets and their associated catcher foils were detected with a 114 cm a Ge(Li) detector available at our centre (VECC). In most of the cases the 7-rays used in the yield determination (listed in tables 1 and 2) stand out very prominently in the spectra and did not pose any identification problem. The ?-ray spectra from the Ge(Li) spectrometers were stored in 4096 channels of m e m o r y of a C a n b e r r a multichannel analyzer and were recorded on magnetic tapes. The ND-500 and SUPER-32 computers were used to analyze the 7-ray spectra stored on magnetic tapes. The methods of analysis of the 7-ray spectra and the efficiency calibrations of the detector were the same as reported in I-9-11].

The nuclear data necessary for the evaluation of the cross sections are presented in tables 1 and 2. The half-lives of the radioactive atoms are taken from the chart of nuclides, the ?-rays energies and branching ratios are taken from the table of isotopes [20]. In tables 1 and 2 only those ?-rays are listed which were chosen for the calculation of the cr0ss-sections. Also included in tables l and 2 are reaction Q-values which however excludes cluster emission. Thus in the case of or-emission 28"3 MeV will have Table 2. Half-lives, )'-energies, branching ratios of the ),-decays and Q-values for

•-induced reactions on V and Re.

Half- E~ I v Q-values

Nuclide lives (keY) (abs) Reaction (keY)

S4Mn 312.2d 835.0 1 . 0 0 0 5W(a,n)S4Mn - 2292-2 52Mn 5"590d 774.2 0.900 5W(a, 3n)SZMn - 23285.5

935"5 0.945 1434.1 1-000

SlCr 27-70d 320"1 0 - 1 0 2 51V(a, p3n)SlCr - 29829"6 4sV 15"98d 983"5 1 " 0 0 0 5W(~,2p5n)4SV - 60237"7 1312"0 0 " 9 7 5 5W(~t, ~t3n)4SV - 31941"8 47Sc 3"420d 159"0 0"685 5 tV(~t, 4p4n)4~Sc -66885"4 5 W(~', ~,2p2n)47Sc - 38589.5 sW(~, 2~t)47Sc - 10293-6 46Sc 83"80d 889'3 1.000 s W(~, 4p5n)46Sc - 77528.7 1120.5 1-000 5 W(~t,ct2p3n),6Sc - 49232.9

5 I V(o~ ' 2 ~ n ) 4 6 S c - 20937"0

5 IV(~t, 9Be)46Sc - 19363"5

19°Ir 11.78d 186.7 0 . 5 2 8 tSVRe(at, n)lg°Ir - 10150.4 557.7 0"303

189Ir 13.10d 245.0 0.062 1SVRe(~, 2n)lS9Ir - 16481.8 'SSOs 93"60d 646"1 0 " 8 1 0 'SSRe(a, p3n)'SSOs - 30093.2 lSSRe(~t,4n)lSSIr - 33376"6 lS6Re 90"64d 137"2 0 " 9 3 0 lSSRe(ot, 2pn)lS6Re -22117-5 lS4Re 38'05d 111"2 0 " 1 7 2 lS5Re(ct, 2p3n)lS4Re -35975.3 792.1 0 - 3 7 6 lSSRe(ct, ~tn)lS4Re - 7675-0 894"8 0" 156

903"3 0"381

lS3Re 71"20d 162'3 0 " 2 4 6 lSSRe(~t, 2p4n)lS3Re -42450.6

291"7 0'032 lS~Re(ct, ~t2n)~S3Re - 14150.6

230 Pramana- J. Phys., Vol. 40, No. 3, March 1993

M e a s u r e m e n t o f excitation functions and mean projected recoil ranges to be added to the listed Q-values. Q-values were calculated by using the atomic mass table of Wapstra and Audi [21].

2.1 Recoil range measurements

Several techniques have been devised to measure the momentum of the recoiling nuclei. In the present' work the linear momentum transfer characteristic in the a-induced reactions on 59Co and 5 ~V, were obtained employing the classical method of thick-target thick-catcher recoil range measurements [15-17]. If the target and catcher foils are perpendicular to the beam axis and the target thickness is larger than the maximum observable recoil range and let x be the fraction recoiling forward, then ( 1 - x) is the corresponding fraction recoiling backwards, N the number of residual nuclei produced per unit length of the target thickness, RF and R B the forward and backward ranges, T the target thickness and A F, A a and A r the activities induced in the forward and backward catchers and in the target, then it easily follows

A F = x N R F ; A B = (1 - x ) N R B ; A T = N T - A F - - A B hence

AF/(A F + AT) = x R r / [ T - R~(1 - x)].

If x is close to unity one can neglect the last term in the denominator which is small in comparison with the target thickness and then one obtains

R v = T . A F / ( A r + AT).

The fraction x can be determined if one uses targets of thickness considerably smaller than the projected ranges. This relation has been used in this work to measure the mean forward range in c~-induced reactions in cobalt and vanadium targets.

In order to obtain information about the linear momentum of the recoil products, their ranges were converted to velocities parallel to the beam direction (l/p) with the help of range-energy relation de/dp given by Lindhard, Scharff and Schiott [22]. The stopping power de/dp is the sum of two terms de/dp = (de/dp) e + (de/dp),. For the electronic energy loss, the expression (de/dp) = k~/~ given by Lindhard and Scharff [23] is used. For the energy loss due to nuclear collision the expression {de/dp)n = - c log(~/a + b/e ~ } with c = 0-2, c~ = 1"215, a = 70-0, b = 0.002 and fl = 0.815 was used.

In the dimensionless energy range 2.0 x 10 -3 <~e ~< 10, this function fits the curve given by Lindhard et al [22] to within 2%. In these expression the dimensionless range and energy variables p, ~ and k are defined in the appendix. Some relevant details of the Lindhard et al [22] formalism are presented in the Appendix. The correction for the evaporation velocity vector [ 15-17] was neglected in the calculation of (Vp). In the recoil range limits which are relevant to the present work, the ranges are almost exactly proportional to the recoil velocity as shown above as well as in [24]. It was shown in [25] that under these conditions, and with the assumption of an isotropic distribution of the evaporation vector, the evaporation contribution to the thick target recoil ranges may be neglected to the first order. The correction to (V,) arising from the angular distribution of the recoils (cos ~b>, due to atomic collisions, was calculated by the expression derived by Blaugrund [26] where ~b is the scattering angle due to nuclear collision. The relevant details are given in the appendix.

The technique for the range measurement mentioned above assumes uniform production cross-section for the nuclei throughout the target width in energy units.

Pramana - J. Phys., Vol. 40, No. 3, March 1993 231

M Ismail

In the present work range measurements for two targets SlV and 59Co are shown in tables 7 and 8. The thickness of slV targets corresponds to --- 2.5 MeV in energy units for 6 0 M e V e-beam, whereas the thickness of S9Co targets correspond to - 3.6 MeV in energy units for 60 MeV e-particles. Therefore, in s IV, the cross-section at the far edge does not differ from the average cross-section over the target thickness whereas in 59Co the cross-section at the far edge might differ appreciably compared to the average cross-section over the target thickness. If the bombarding energy is at the rising part of the excitation function as seen from the high-energy side then the range extracted by this method will be larger than the actual range whereas if the bombarding energy is at the declining part of the excitation function then the opposite will be true i.e. the extracted range will be smaller than the actual range.

This is the reason that in SgCo some of the extracted ranges are higher than the calculated ranges. However for completeness these are included in the paper. As discussed in § 4 all the radionuclei produced by e-induced reaction on 59C0 for which the ranges have been measured are due to fusion-evaporation process. Hence range values tell very little about the reaction mechanism for this nucleus.

3. Experimental results 3.1 Experimental error

In tables 3, 4, 5 and 6 the experimental cross-sections are presented along with absolute errors. The absolute error consists of uncertainties due to target foil thickness ( + 1%), the beam current integration ( + 1%), the detector efficiency ( + 5%) and the analysis of the ~-ray spectra, (statistical uncertainty) generally ( ~< 2%). The uncertain-

Table 3. Experimental cross-section for the s-induced reaction with fluorine.

Cross-section for the product (mb) E+__DE

(MeV) 22Na

8"91 ___ 0"49 3"82 + 0.31 10"26 _+ 0"38 133"55 + 10-68 12"33 + 0"42 204"36 + 16"35 13"53 + 0"42 237"98 + 19-04 15"52 + 0"34 235-26 + 18.82 16"39 _ 0"37 190"64 + 15"25 17"81 -t-0"28 149'41 + 11"95 18"90 + 0"28 106"42 _ 8"51 20"08 + 0-30 76-19 + 6"10 21-05 ___ 0-32 61-72 _+ 4-90 22.11 + 0"28 49-02 ___ 3"92 23"18 + 0"38 40'20 + 3-20 23"91 + 0-32 40"73 _ 3"26 25"32 + 0"34 23-67 + 1"89 25'70 + 0"22 22"59 + 1'81 27-30 _ 0'26 19'28 __+ 1-54 28-87 + 0"25 16"24 + 1-30 30"39 + 0"23 15"66 + 1"25 31"79 + 0"23 9"98 ___ 0'08

232 Pramana- J. Phys., Vol. 40, No. 3, March 1993

,¢ ,¢ ,¢ O Z ,o ^{Iw I'O L~O L~}

Table 4. Experimental cross-section for the ~-induced reaction with vanadium. Cross-section for the product (rob) E +- DE (MeV) S4Mn S2Mn 51Cr 4sv 47Sc 46Sc 58-12 ___ 1.28 55-58 +- 1-32 54.87 +- 1"34 52'93 _+ 1'37 51-51 +- 1-39 49-96 +- 1-42 47"57 ___ 1"49 46'04 +- 1"52 44-14 +- 1.56 42-03 -t-_ 1"60 40'96 +- 1-65 40-05 + 1-65 37'62 +- 1"75 37"45 _+ 1"75 36"03 +__ 1.78 35"69 + 1"82 33"93 -+- 1"87 33"83 _+ 1.87 32'91 +- 1-92 31-82 + 1"92 30"49 +- 2"03 29'87 +- 2"08 27.87--,2"18 27-55 +- 2-18 26-91 +- 2"19 25-66 _ 2'24 23"32 _ 2"38 21"26 + 2.47 18'25 + 2.85 15'36 +- 3-01 12-08 _+ 3'33

14'18 +- 1"13 13"29 +__ 1-06 17'84 +- 1 "43 20-66 +- 1.65 25"98 +- 2"08 26-49 +- 2-12 49-68 +- 3-77 55'51 _+ 4.44 70'75 +- 5"66 207-70 + 16.62 307"74 _ 24"62 512"04 +- 40-96 359"53 +- 28.76 13.88 +- 1"11

67.73 ± 5.42 465'18 + 21-49 65.32 + 2.13 3"87 +__ 0-31 19'67 _+ 1.57 92'65 + 7-41 477-92 + 38"23 44.89 +- 3"65 4.05 _ 0"32 102'21 + 8"18 483-91 +_ 38.71 45.46 ± 3"65 20-93 +_ 1"58 120-35 _ 9-63 391"54 ___ 31-32 22.02 +- 1"76 4"40 ___ 0-35 149"08.-_ 11"93 370-18.-,29"61 14"60.-, 1"19 14-55.-, 1"17 154"14.-,12-33 286.65+_22"93 7-1.-,0'56 4.70.--0"38 216-72.-, 17"34 200"42__ 16-00 1'91 ___0-15 5"77.--0"46 7-27.--0"58 243"09 _ 19.45 6"00 +- 0-48 273'10 + 21'85 71"39 +- 5"71 6-20 _ 0"50 287-17 +- 22"97 5.37 +- 0-43 287"27 __+ 22-97 33" 10 +- 2"65 4"84 +- 0"39 283-04 +- 22'64 12"73 ___ 1-01 236'14 _ 18"89 2.51 +- 0'20 147"24 + 11"77 3-77 +- 0"30 96-98 + 7"76 0'75 + 0-06 76"90 -I- 6.15 0.47 +- 0.04 8" 15 _+ 0"63 0-45 ___ 0-04 1"90 ___ 0-15

e~ e~ g~

tO g I gr 0 2 .o

Table 5. Experimental cross-section for the ~-induced reaction with cobalt. Cross-section for the product (mb) E+_ DE (MeV) S4Mn S6Co STCo SSCo 6°Co 62"74 + 1"76 23-31 +___ 1"86 61-73 _____ 4"94 94-10 -I- 7"53 178"01 _____ 14-24 59-01 _____ 4"72 58-45 _____ 1-84 31"47 +- 2-52 47"56 -I- 3"80 131"08 -I- 10"5 125-43 + 10-03 72-63 _____ 5"81 57-80 +- 1"87 32-97 ± 2"64 39"48 _____ 3"20 138"70 _____ 11"2 120-44 +- 9"68 72"46 _____ 5-84 54-04-t- 1-96 34"46-t-2"76 19"71 _____ 1-58 183"41 -I- 14-7 111"94+8"95 79"33_____6"35 50"00---- 1"96 25-49---2"04 3-88_____0"31 205-32--- 16"5 120-18--,9-62 76"27_____6"16 49-20+2-10 20"92__+_1"67 1"75--,0-14 197.53 +- 15;8 130"58+10"40 68"84--,5"51 45"80 ____. 2"21 10-63 __ 0"84 0"17 _____ 0"03 184"03 +___ 14"7 162-70 _____ 13"02 54"67 _____ 4-40 44-t4-t-2-26 3"18+0-25 0"096+0-01 122"14+9-77 198"50+15-88 29-15--,2"33 41-30 _____ 2"37 1-76 ± 0-02 0-17 + 0"03 101-39 __ 8"20 228"07 +- 18-25 27"84 _____ 2"32 38"62 +- 2"48 9-32 _____ 0-75 8"81 +- 0"70 225"43 -t- 18-03 2-76 +- 0"22 36-40____.2"58 7"12±0.60 224-41 _____ 18"00 2"82_____0"24 31'10 __+ 2"87 93"96 + 7-50

Table 6. Experimental cross-section for the or-induced reaction with rhenium. g~ Cross-section for the product (mb) E-I-DE (MeV) lS4Re lS3Re 185Os IS6Re 19°Ir 191Ir t~ ~ 59.94+_ 1.47 67.05+5-36_ 90.92+7"27 ... 831.18+66"49 13-04+ 1.04 1-39+0-11 34.54+2.76 g~ 57'90+1"50 62"46-1-5-00 69-19+5"54 830-11+66"41 56-99+1"51 59-13+4"73 57"82+4"63 931'84+74"55 12"07+0"66 1'56+0"12 33-68+2'69 ,~ 54"95 + 1"55 54"91 + 4"39 56-82 _ 4"55 1042-26 + 83"38 ~r 53"93+_1"59 48"20_+3"85 51'40-t-4"10 1141"15+91-28 9"62+-0'90 2'52+0-22 33"33+2"66 ~" 51-79 ± 1'61 47-01 +_ 3-76 48"41 + 3-87 1282-10 4- 102'57 3-00 _ 0'24 29-29 ±_ 2-34 = "< 50'77__+ 1'63 36'49+2'91 40'21+3'22 1024'63+81"97 8"74+-0'70 2'37+0'19 44'99+3'60 O • -- 48.42 + 1"68 32.92 + 2-63 41"87 + 3'35 999-40 + 79-95 3"62 + 0"29 35"35 + 2"83 47-40 ± 1"70 25.00 + 2.00 22.49 _ 1.80 558"06 + 44.64 6-54 +_ 0"52 2-97 4- 0-23 62.54 + 5-00 ~Z 45"04 _+ 1.76 22"79 _ 1-82 12-79 + 1-02 431-34 _+_ 34-51 3-77 + 0"30 53-62 + 4"29 © 43"91 + 1"79 19-54+ 1-55 109.38+8-75 4-84+0-39 4"17+0-33 83"78+6'70 = 41-45 ± 1"85 16.00 4- 1"28 49-02 _ 3-92 6-03 _ 0-48 87-01 4- 6-96 40"22 + 1"89 8"83 + 0-71 2.79 + 0"22 6"08 + 0.49 167-36 + 13"39 37"54 ___ 1"96 7-17 + 0-11 8"29 4- 0-66 255'69 4- 20"45 "~ = , 36-30 ± 2'00 1-44 4- 0" 11 8"76 + 0"70 498-09 4- 39"85 ~. 33'50+2'10 12.994-1-04 649.00+51-92 32-15 ± 2"15 16"53 _ 1"32 379-49 +- 30"36 29-13 ± 2.27 23-61 + 1"89 220-52 +- 17.64 27'86 +_ 2.34 7"76 _ 0-62 19.57 ±_ 1.57 24-40 ± 2.51 0-76 + 0"06 ¢~ bo

M lsmail

300-0

240-0

3 v E

Z 180-0

o i-. o laJ £/3 120.0

I 03 03 o n,- 80.0

I L l o . o l I I ,

0"0 8"0

19 2 2

F ( O , n ) No

I I J I I I I ] t I = 1 " ~

1 6 . 0 2 4 . 0 3 2 " 0 4 0 . 0

E N E R G Y ( M e V )

Figure 1. The total residual cross-section in mb for the reaction

19F(~,n)22Na

rll symbols] plotted as a function of ~-particle bombarding energy. The solid line is geometry dependent hybrid model (GDH) with initial exciton configuration n o = 4, n.--2, np= 2, n h = 0 or in short (4/2/2/0). The dashed line is the hybrid model calculation with exciton configurations (4/2/2/0). The theoretical curves are normalized to experimental values at the maximum cross-section point with normalization constant N = 0"93 for both the curves.

ties caused by the large size of the irradiation area and the non-uniformities of the target contribute about 5?/0 to the average error of the cross-section. However, the above mentioned average error values do not include tile uncertainties of the nuclear data used in the analysis.

3.2 Integral excitation function

In table 3 (figure 1), table 4 (figure 3a, b), table 5 (figure 4a-4c) and table 6 (figure 5a, b) our experimental results for the e-induced reactions on F, V, Co and Re targets are summarized. The uncertainties given for the energies include those of target thickness and beam energy resolution only. The cross-sections are in millibarns and the uncertainties are ~ 8?/o. Our results for or-induced reaction on vanadium are in good agreement with those of Michel et al [27] and references therein. With respect to cobalt, our results are in fair agreement with those of Michel and Brinkman [28] and Jastrzebski et al [14] in the overlapping region. The comparison could not be made for rhenium data, since no data exist in the literature. The measured recoil ranges for e-induced reaction on vanadium and cobalt are presented in tables 7 and 8 respectively. The recoil ranges for full momentum transfer are also presented with ( + ) marks and corresponding recoil energies are marked with asterisk (.) marks, alongwith the measured recoil ranges.

4. Comparison with theoretical predictions

A rigorous theory of nuclear reaction for which calculations can be performed to describe mass, angular and energy distribution data from intermediate energy collision with complex particle is presently not available. A simpler compound nucleus model 236 Pramana - J. Phys., Vol. 40, No. 3, March 1993

Measurement of excitation functions and mean projected recoil ranges

4 0

27 24

AI ( at , ~ p n ) No "[

32 no n . n . % . I~ TIll

GDH I0 5 5 0 ..-. - - - - - - .

HYB I0 5 5 0 /~'"T~':J" ] - " ' " ' " - ~ ' - "

....... . Y B B , , o

2 , - - 6 , 2 0 h" . . .

5 //

I

8

i

.'/

0 Im IR

30 38 46 54 62 70

E a (MeV)

Fignre 2a. Excitation function for 27Al(ct, ct2pn)24Na. The solid line is GDH model calculation with (10/5/5/0), the dashed line is hybrid model calculation with (10/5/5/0) the dotted line is hybrid model calculation with (8/4/4/0) and the dashed-dotted line is hybrid model calculation with (6/4/2/0). The normalization constant N = 1 for all the four curves.

[29] is clearly not applicable above 10 MeV/nucleon owing to large probability for pre-equilibrium processes. In the pre-equilibrium models on the other hand, it is difficult to extract kinematic information [13]. Most of the nuclear reaction models [1-7, 30, 31] to treat the pre-equilibrium phase of reactions leading to the formation of a compound nucleus are semi-classical in nature and have been used with considerable success in describing experimental data pertaining to the equilibration process, mainly the forward-peaked hard component observed in the continuous spectra of light ejectiles and the high energy tails seen in the excitation functions of activation cross- sections. However, most of these models employ one or both of the two basic concepts:

the intranuclear cascade model [INC] and Griffin's statistical model of intermediate structure [5] (SMIS). The integral excitation functions ef ~-induced reactions have been discussed by several workers [1-7, 12, 13] considering models of the compound nucleus as well as of pre-equilibrium reactions, as mentioned above. They conclude that the theory of pre-equilibrium reactions is helpful in explaining the mechanism of ~-induced reactions. The hybrid model for pre-equilibrium reaction was proposed by Blann [1] which provides in some way a marriage between the simple SMIS model of Griffin [5] and the INC model using the more elaborate master equation approach due to Harp et al [6] and Harp and Miller [7]. However, there were some shortcomings in the hybrid model. It gives incorrect cross-sections and spectral distributions when applied to nucleon induced reactions at medium energies. The comparison with the INC model indicated that in the hybrid model deficiencies Pramana- J. Phys., VoL 40, No. 3, March 1993 237

M lsmail

J¢l v E o Z t - O LIJ O3 O3 (/) O n- O

5 0

2r / .2CYn ~.22 T |

i AI (Gf,,It, le]gl) No T ) I t I - ~ " ~ , . 'rlonono nh T I/I 'I' %,

. - - GOH ,o 5 5 o J. ,~ . . l " l ~ T . . \

---HYB ~05 5 0 TII" ~ I .".. A

40 . . . HYB 8 4 4 0 .~'"'J" 'I' I r "J - - - HYB 6 4 2

3 0

~.,.~

I 0

O l I ~ ' ~ 1 I I I I i I I I l I i I i ~ i

3 0 38 4 6 5 4 62 70

E (MeV)

(2

Figure 2h. Excitation function for 27Al(~, ~2p3n)22Na plus 27A1(~, 2~n)22Na. The solid line is G D H model calculation with (10/5/5/0), the dashed line is hybrid model calculation with (10/5/5/0), the dotted line is hybrid model calculation with (8/4/4/0) and the dashed-dotted line is hybrid model calculation with (6/4/2/0).

The normalization constant is N = ] for all the four curves.

resulted from the failure to take properly the enhanced emission from the nuclear surface. These deficiencies were partly rectified by reformulating the hybrid model as a sum of contributions, one term for each entrance channel impact parameter. In this way the diffuse surface properties sampled by the higher impact parameters were crudely incorporated into the precompound decay formalism in geometry dependent hybrid model (GDH) by Blann I-2]. However, it has been shown I-2] that this measure changes the predicted emission cross-section about the same as would a factor of 2 increase in the mean free path in the formulation of the hybrid model. In the present work our excitation functions are calculated on the basis of hybrid model 1,1] and geometry dependent hybrid model 1,2] using the program Alice/85/300 [32] on the ND-500 and Super-32 computer at our centre. The calculations were done in 2 MeV steps from 10.0 to 65.0 MeV.

The statistical part of the overlaid Alice can account for a large variety of reaction types. Besides evaporation of neutrons and protons 1-33] also dusters such as deuteron and ~-particles can be considered. The binding energies and Q-values used in the present code were based on experimental masses. The Alice/85/300 code stores experimental masses in a data file. Whenever the nuclear masses are not tabulated then these were calculated from the Myers and Swiatecki mass formula 1,34, 35], liquid drop masses with pairing for some and shell corrected masses with pairing for some nucleus. We have used the option in the default version of G D H whereby only 238 Pramana - J. Phys., Vol. 40, No. 3, March 1993

Measurement of excitation functions and mean projected recoil ranges

700.0

,5600

E

Z 420-0 0

I -

(..3 I.IJ 03 280.0 _! Or) 03

0 0~

140"0

0-0 O.0

I 1 1

lII SlY ( a , n ) S4Mn

Sir (a, P3n)S! Cr

/

/

I;;"O 24"0 36"0 48.0 60"0

E N E R G Y ( M e V )

Figure 3a. Excitation functions for slV(~, n)~4Mn and s tV(~, p3n)SlCr. The solid lines are GDH model calculation with (4/2/2/0) and N=0.614 and 0.911 respectively. The dashed line is the hybrid calculation with (4/2/2/0) and N = 0.614 and 0-814 respectively.

,.O

E

Z 0

I -

L) UJ 03 !

03 03

0 IX (,J

4 0 0 " 0 f ' 320"0 f

IIII 51V(=,3n ) 52Mn

+ 5Iv (~t, It 3n)4e v

240.0 r- ~" ~-- ,// x ~ x

160.0

80"0

0-0 ~-~ @ I I i I I I I l I

25.0 320 39'0 46.0 53-0 60.q

E N E R G Y ( M e V )

Figure 3h. Excitation functions for sW(o(, 3n)S2Mn and stV(~, ~(3n)*SV. The solid lines are GDH model calculation with (4/2/2/0) and N =0.780 and 1.742 respectively. The dashed line is the hybrid calculation with (4/2/2/0) and N = 0.712 and 1.170 respectively.

Pramana - J. Phys., Vol. 40, No. 3, March 1993 239

M 1small

300

240

v

Z O -

180 ~-- ( J LJJ 09

I 120 Or) Or) 0 r r ( j 6o

o l 3o

~¢ Z~ 57Co

I I

37 44 51 58 6@

ENERGY(MeV)

Figure 4a. Excitation functions for SgCo(~, ~t3n)SeCo and SgCo(ct, 2p4n)STCo plus SgCo(ct, ct2n)S~Co. The solid lines are GDH model calculation with (4/2/2/0) and N = 1-000 and 1-367 respectively. The dashed lines are hybrid calculation with (4/2/2/0) and N = 0.614 and 1"07 respectively.

I00.0

59C0 ( e, 2pn )6°C 0

- .T. 59 ~ Zp3n~4 .T

8 0 0 T Co ( O ~ , ? , . Q ~ [ Mn T t - - ~ l k ~ , ~ .

E

/ I ~ ' \ I T M 6 0 0 --

Z

O F I" ..

I--- t.) b.l o0 40.0

~ 200

o.~ ! = ~ J ~ F ~ , ~ , t ' l , , I , , , I , , ,

30.0 3~.o 44.0 5,-0 ss.o ~-o

E N E R G Y ( M e V )

Figure 4k Excitation functions for SgCo(~t, ~t2p3n)~4Mn plus 59Co(~t, 2~m)54Mn and 59Co(ct, 2pn)6°Co. The solid lines are GDH model calculation with (4/2/2/0) and N = 5.400 and 1.270 respectively. The dashed lines are hybrid model calculation with (4/2/2/0) and N = 3.700 and 1"520 respectively.

the first collision is localized according to the impact parameter [36] with all the higher order precompound terms being treated by the hybrid model i.e. using nuclear densities averaged over the nlscleus and independent of impact parameter. This is reasonable because the excitons can sample nearly the entire nuclear volume after a 240 Pramana - J. Phys., Vol. 40, No. 3, March 1993

Measurement of excitation functions and mean projected recoil ranges 300.0

240-0

180.0

120-0

.Q

E z o t- c) uJ o3

I

03 0 nr U 60-0

0 " 0 I

2O-O

,ctn

SSCo (Gt,Zp3n)Saco

, ~--~-

29'0 38"0 47'0 56.0

1

65.0

E N E R G Y ( M e V )

Figure 4e. Excitation function for 59Co(;t, 2p3n)SaCo plus SgCo(;t, ;tn)SaCo. The solid lines are G D H model calculation with (4/2/2/0) and N = 1.333 and the dashed line is hybrid calculation with (4/2/2/0) and N = 1.226.

1500.0

A J O v E z o I-- L) LU (I)

I

03 0') 0 n,"

(.) 12000

900-0

600.0

300-0

0.0 20(

(, (,

l e 5 165

Re ( a,4n ) Ir j

187

Re{a,2n) tr 169 ~ / i~T 1 ~

I

29"0 58'0 470 560 85"0

E N E R G Y (MeV)

Figure 5a. Excitation functions for laSRe(~t, 4n/p3n)lSSlr/laSOs and 187Re (~t, 2n) 1S9Ir. The solid lines are G D H model calculation with (4/2/2/0) and N = 0-984 and 0-684 respectively. The dashed lines are hybrid model calculation with (4/2/2/0) and N = 0-927 and 0.683 respectively.

Pramana - J. Phys., Vol. 40, No. 3, March 1993 241

M lsmail

50.0

24-0

v E

Z 18.0

O I - I.IJ (1) 12-0

I O3 O n,"

0 6.0

I N III m S R e ( a , 2 p n ) Re

,.2,.,

0"(3 _

20"0 29-0 38"0 47"0 56"0 65"0

E N E R G Y (MeV)

Figure 5b. Excitation functions for XSSRe(=, 2pn)tSeRe and tS~Re(=, n)t9°Ir. The solid lines are GD[-I model calculation with (4/2/2/0) and N = 1.625 and 0"522 respectively. The dashed lines are hybrid model calculation with (4/2/2/0) and N = 3.800 and 0-522 respectively.

100-0

80-0 ..Q

E z 60.0 o I - (D LLJ O3 40-0

0 n-" 20.0

O

185 ~, rYtl 1|4

Re (~'.2p~n) Re

A,J 2n ~183 I~ lllSRe ( G . 2p 4n / Re

##

I i I ! I I I t =

37.0 44..0

f

O O t I I i i = I , I =

30.0 51-O 58.0 65.0

E N E R G Y ( M e V )

Figure 5e. Excitation functions for tSSRe(~t,2p3n)lS4Re plus lSSRe(~t,~m)lS4Re and lSSRe(~, 2p4n)tS3Re plus lSSRe(=, ~2n)lS3Re.

single scattering since the mean free path (mfp) values are ~ 4-74 fm. The inverse cross- sections were calculated using the optical model subroutine of Overlaid Alice [32], where the optical model parameters were those of Becchetti and Greenlees 1-37]. The Fermi level density used is of the form

p(u)

s/4"a-

where u is residual nucleus excitation, a is the level density parameter taken as

A/9

Measurement of excitation functions and mean projected recoil ranges Table 7. Experimental range for the or-induced reaction with vanadium.

Recoil Range (/lm) and recoil energy of the product

E + DE energy

(MeV) (MeV) S2Mn 5tCr *sv ~6Sc

58"12 _ 1"28 4"227 1'0112 1'0758 0"8629 1"2130 1"267+ 1"298+ 1"255+ 1"312+

3"996, 3"919, 3"689, 3'535, 54'87 + 1'34 3"991 1" 1761 1'0844 0"6909 1"2499 1"210+ 1-232+ 1'198+ 1"246+

3'773, 3'700, 3"483, 3-338, 51"51 _ 1"39 3'746 1"1714 0"9641 0"5055 0"9216 1'138+ 1'161+ 1"128+ 1"181+

3"542, 3"474, 3'269, 3"133, 47'57 + 1"49 3"460 0"9552 0"6453

1-068+ 1-081 + 1"060+ 1"105+

3-271, 3-208, 3-019, 2"894, 44"14 + 1'56 3'210 0 - 8 6 2 9 0"3496

0-9982+ 1'012+ 0"9879+ 1"028+

3-035, 2"977, 2"802, 2"685, 40"05 !-_ 1-65 2-913 0-6695

0-9076 + 0"9321 + 0-9027 + 0"9501 + 2"754, 2-701, 2"542, 2"436, 35"69 _ 1"82 2'596 0-3185

0"8183+ 0"8384+ 0-8118+ 0-8548+

2-454, 2"407, 2'265, 2"171, The calculated recoil range for full momentum transfer are marked with symbol (+) and the corresponding recoil energies are marked with symbol (,).

energy shift, with either a backshifted or standard pairing shift option. We have used the standard option.

In the a priori formulation of the hybrid and geometry dependent hybrid model, the intra-nuclear transition rates are calculated either from the imaginary part of the optical model or from the free nucleon-nucleon scattering cross-section [38]. The use of optical potential in calculating intranuclear transition rates for pre-equilibrium decay models offers distinct advantages at least in principle over the nucleon-nucleon scattering approach. Specifically, the parameters of the optical potential have been determined from the results and trends of a large body of experimental data. The mean free path values are therefore based on experimental measurements in nuclear matter as opposed to the extrapolation of free scattering cross-sections to the nuclear environment. Secondly the question of possible errors in nucleon-nucleon scattering approach due to failure to consider recoil momentum effects is avoided by using the optical potential. Becchetti and Greenlees [371 have analysed vast amount of data to find a best set of optical model parameters for nucleon induced reactions. But for particle energies exceeding 55 MeV the optical model parameters of Becchetti and Greenlees [37] are no longer applicable and thus at higher energies the calculation of the mean free path for intra-nuclear transitions are calculated from n u c l e o n - nucleon scattering cross-sections.

The mean free path multiplier 'k', which is a kind of a free parameter, was introduced Pramana - J. Phys., Vol. 40, No. 3, March 1993 243

M lsmail

Table 8. Experimental range for the a-induced reaction with cobalt.

Recoil Range (/~m) and recoil energy of the product

E + DE energy

(MeV) (MeV) 5*Mn 56C0 STCo 5SCo

62"74 + 1-76 3'983 1"1316 0"7189 0"7805 0"4611 0"7837+ 0'7520+ 0"7708+ 0"7867+

3"414, 3'541, 3"604, 3'667, 58"45 ___ 1"84 3'711 1"0819 0"5767 0 " 8 5 1 4 0"3823

0-7318+ 0"7085+ 0"7183+ 0-7337+

3"181, 3'299, 3"358, 3'417, 54"04 _ 1"96 3'431 0"8937 0"3559 0"8199 0"4646 0"6838+ 0"6563+ 0"6705+ 0"6816+

2"941, 3'050, 3"104, 3'154, 49"20 + 2"10 3"124 0"6519 0"6946 0"6721 0"6283+ 0"6021+ 0"6146+ 0"6254+

2"678, 2'777, 2"826, 2"876, 44"14 + 2"26 2'803 0"3323 0"7227 0-5661 + 0'5450+ 0"5553 + 0-5671 + 2"402, 2'491, 2"536, 2"580, 38"62 + 2"48 2"452 0"0415 0"5163 0"4985 + 0-4794 + 0"4894 + 0"4987 + 2"102, 2"180, 2'219, 2"257, The calculated recoil range for full momentum transfer are marked with symbol (+) and the corresponding recoil energies are marked with symbol (,).

by Blann [1] in hybrid model to account for the transparency of nuclear matter in the lower density nucleus periphery. Considerably better agreements at the high energy portion of the excitation functions are shown in figures 4-18 of [11] for the results with k = 2.0 compared to k = 1.0 which implies a mean free path (mfp) multiplier for nucleon-nucleon scattering which is k = 2 times the values given in [39]. In the present work considerably better agreement at the higher energy portion of the excitation function are obtained for the G D H model. These results are in agreement with Blann's findings [2] regarding the enhancement in cross-sections in G D H model are about the same as would a factor of 2 increase in the mean free path in the formulation of the hybrid model.

With respect to initial configuration Blann and Mignerey [40] used no = 4 (nn = 2., np = 2, nh = 0) to calculate S9Co(a, p) spectra. Gadioli et al [30, 41] have also discussed this point in detail and recommended the general application of n o = 4. Evidently an initial exciton no = 4 (n, = 2, np= 2, nh = 0) configuration which is equivalent to a break-up of the incoming a-particle in the field of the nucleus and the nucleons occupying excited states above the Fermi energy gives a better description of the excitation function compared to other configurations for the a-particle bombarding energies up to 65.0 MeV. Therefore we have used mostly n o = 4 (n~ = 2, nv = 2, nh = 0) configuration in most of our calculations. The theoretical values shown in the figures are multiplied by a factor so as to match the experimental data at the maximum cross-section point. The multiplying factors are given in figure captions. The multi- plying factors also indidate the quality of fit between experimental and theoretical 2 4 4 Pramana - J. Phys., Vol. 40, No. 3, March 1993

Measurement of excitation functions and mean projected recoil ranges values. In general the hybrid model fits the excitation functions reasonably well taking its limitations into account.

The relative weights of the pre-equilibrium and equilibrium components needed to reproduce an experimental spectrum for particles of type v is the fraction fv of pre-equilibrium emission for particle of that type [40]. However, the fraction of pre-equilibrium particle emission for proton and neutron obtained from the analysis of data are not directly comparable because of the presence of the Coulomb barrier for charged-particle emission. The Coulomb barrier tends to cut-off the low energy portion of the proton spectra thus reducing the number of equilibrium protons. There is relatively little effect on the number of pre-equilibrium protons since these tend to be emitted with fairly high energies. The net effect is that as the mass of the compound nucleus increases, the height of the Coulomb barrier increases and the ratio of the pre-equilibrium to equilibrium proton emission is increased. It is therefore more meaningful to look at the integrated pre-equilibrium neutron cross-section plus the pre-equilibrium proton cross-section divided by the total compound nucleus cross- section. This quantity is designated as f. The predicted variation of the fraction of the pre-equilibrium emission f as function of a energy for all targets as predicted by hybrid and GDH model are presented in figures 6a-6e alongwith the total equilibrium and pre-equilibrium cross-sections. These quantities are calculated using the code Alice/85/300 by Blann [32]. However, the code does not provide the fraction of pre- equilibrium emission separately for each reaction channel. These results are for initial configuration (4/2/2/0) for F, V, Co and Re targets, whereas for Al the initial exciton configuration is assumed to be (10/5/5/0). The results for the Re isotopes lSSRe and ISTRe are almost similar, therefore, the results for only laTRe are shown. The pre- equilibrium fractions are multiplied by a factor of 1000 and then plotted. The total pre-equilibrium cross-section for AI is multiplied by a factor of 4.

The experimental ranges are compared with the expected ranges for compound nucleus production in tables 7 and 8 for ~-induced reaction with vanadium and cobalt respectively. The recoil energies are marked with asterisk marks which are calculated assuming same recoil velocity as that of the compound nucleus. The theoretical ranges as predicted by the range-energy theory of Lindhard et al [22] corrected for atomic scattering by the theory of Blaugrund [26] are marked with plus marks. The excitation functions are generally consistent with a full momentum transfer mechanism with some exceptions for example, the reaction s lV (~,~3n)4V and high energy shoulder of the reaction 51V (ct, 3n)SZV.

In figures 1 to 5 the excitation functions are fitted with the hybrid and GDH model calculations using the code Alice/85/300. The calculated cross-sections are the sum of equilibrium and pre-equilibrium cross-sections. Broadly speaking the peak in the excitation function are largely due to equilibrium emission whereas the high energy shoulders are largely due to pre-equilibrium emissions. For most of the excitation functions shown in figures 1 to 5, the hybrid and GDH models fit equally well except for a few cases where GDH fits the high energy shoulders better than hybrid model.

As shown in figure 6a-6e near the threshold the emission is mostly from an equili- brated nucleus with very little contribution from pre-equilibrium emission. As the bombarding energy increases, the contribution from pre-equilibrium emission gradually increases and becomes appreciable only after the bombarding energy has been increased to 20 MeV or so above threshold. The difference between hybrid and GDH model also increases with increase in bombarding energy above threshold.

Figure 1 shows the fit for

19F(0t, n)22Na

Pramana - J. Phys., Vol. 40, No. 3, March 1993 245