Proton emission in α-induced reactions at 43 MeVnucleon

Nuclear Physics A408 (1983) 359-371 @ Noah-Holland ~bIishing Company

PROTON

EMISSION IN a-INDUCED AT 43 MeV/NUCLEON

B. LUDEWIGT, Insiitut

ftirKerphysik

REACTIONS

R. GLASOW, H. LGHNER and R. SANTO der Vniversitcit Miinster, D-4400 Mtinster, W. Germany

Received 25 May 1983

Abstract: Inclusive proton spectra and proton-proton correlations have been measured from a + ‘sNi and a + ig7Au reactions at energies E, = 100 MeV and 172 MeV. The inclusive spectra are compared to results of a simple model assuming local equilibration of the energy transferred to the target m&eons. This model describes the energy and anguhtr dependence sufftciently well at angles 2 40”. Due to finite number effects, it also explains the occurrence of differences between in-plane to out-of-plane pp correlations. In addition, the measured coincidences indicate contributions from quasifree pp scattering.

E

NUCLEAR REACTIONS ‘*Ni, i9’Au(a, pX), E = 100, 172 MeV; measured o(E; E,, f?), pp’-coin. ; deduced reaction mechanism.

1. Introduction

At projectile energies up to some 10 MeV, (a,pX> reactions may be classified into three groups distinguished by reaction time and number of participating nucleons: There are fast direct reactions (e.g. stripping or pick-up reactions, projectile fragmentation) involving only a few nucleons, whereas in compound nucleus reactions the excitation energy is shared among all nucleons in a large number of individual nucleon-nucleon collisions on the way to an equiiibrated compound state. The reactions in the transition region between these two extremes, known as preequilibrium reactions become more important with increasing projectile energy. They are often described in terms of the exciton model ’ 3‘) or the hybrid model 3). These models assume a mean free path large compared to the diameter of the target nucleus 4), an assumption only valid up to a certain energy. At energies beyond 20 MeV per nucleon above the Coulomb barrier the projectile velocity approaches the Fermi velocity in nuclei. In this energy region a change of the reaction mechanism is conceavable since the Pauli blocking effect becomes less stringent and the nuclear mean free path decreases rapidly ‘). 359

360

B. Ludewigt

et al. 1 Proton emission

In this paper the proton emission is regarded from a point of view different from the exciton model: The hypothesis of a local thermal equilibrium, which plays an important role in heavy-ion reactions at relativistic energies 7-9) as well as at relatively low energies lo- ’ 3), is applied t o a-induced reactions at E, = 100 MeV and 172 MeV, modifying a model described earlier 14). In particular, it has been investigated to what extent the preequilibrium part of the (CI,p) reactions may be explained by proton emission from a locally excited zone of the target nucleus. Since in nuclear matter at temperatures of about 8 MeV the mean free path of nucleons at energies above the Fermi level is significantly shorter than the diameter of a medium weight nucleus 6), a local excitation may occur. Since inclusive spectra do not provide a very sensitive test of the reaction mechanism at energies discussed here, the correlated emission of two protons has been investigated by an in-plane/out-of-plane coincidence experiment. As to our knowledge these are the first out-of-plane correlation measurements performed in this energy region. In sect. 2 the experiments are described. The local excitation model is explained and compared to the single particle inclusive spectra in sect. 3. In sects. 4 and 5 the coincidence data are presented and discussed in terms of two different model calculations.

2. Experiments The experiments have been performed in a 100 cm diameter scattering chamber using the a-beam from the Julie cyclotron at beam energies of 100 and 172 MeV. The beam current varied from 5 to 200 nA according to the specific measurement. The beam transport system was optimized with respect to the beam halo by replacing the target by an aperture and minimizing the forward-angle scattering. The dectector solid angle was defined by tantalum apertures with thicknesses of 12 mm and 4 mm for detection of hydrogen isotopes and other higher-Z fragments, respectively. Self-supporting 58Ni and 19’Au foils (enrichment 2 99.8 %) of thicknesses ranging from 0.8 to 2.0 mg/cm* were used as targets. Their carbon contaminations, checked by measuring the inelastic and elastic a-peaks, were smaller than 12 pg/cm* for all foils. Charged reaction products (p-l ‘B) were detected with various counter telescopes at lab angles between 0 = 20” and 150”. The telescopes (see table 1) for the proton detection consisted of surface barrier detectors (SB) as AE detectors and Ge(Li) or NaI detectors for the -E-measurement. The energy calibration of the NaI detectors required particular efforts, since the scintillator light output is a non-linear function of the observed energy and, in addition, depends on the particle type due to quenching effects. By measuring the

361

B. Ludewigt et al. / Proton emission

TABLE1 Survey of detector telescope types Detector k,,i, (MeV) (proton) AE

used

in this experiment

AR

E,,, (MeV) (proton)

(msr)

E

1000 pm SB

3 cm Ge(Li)

12

90

50,200,lOOO pm SB

3 cm Ge(Li)

4

90

inclusive spectra 0.09 E, = 100 MeV 0.06 1

200 pm SB

3 cm Ge(Li)

5

50

0.09

2000 pm SB

8 cm NaI

25

150

0.5 >

8 cm Nal 4x2 mm SB 4x2 mm SB 4x2mm SB

12 9 9 9

80 40 40 40

E,=

Tl : T2: T3: T4:

1000 pm 500 pm 500 pm 500 pm

SB SB SB SB

172MeV

coincidence spectra 2.0 1.2 1.3 1.0

protons recoiling from a mylar target in elastic a-scattering, an experimental energy calibration curve was obtained for proton energies up 100 MeV. A calibration function allowing the energy calculation within an error ‘smaller than 2 % has been established by fitting a polynomial to the experimental curve. The energy resolution of the NaI detector was 1.5-2 MeV for 172 MeV a-particles. The reduction of the efficiency due to reaction losses within the NaI detector and scattering out was estimated to be smaller than 10 % up to a proton energy of 80 MeV, and smaller than 20 % up to E, = 130 MeV (the largest p-energy measured). Since the cross section drops off sharply with increasing energy, the lower energy part of the p-spectra (up to 80 MeV) is not affected by the reaction losses at high energies. All signals have been recorded on tape event by event. The particle identification and the generation of the energy spectra have been performed offline. In addition to the single-particle spectra measurement, light particle (p, d, t, a) correlations have been investigated. In this paper we restrict ourselves to pp correlations studied in the reaction “Ni(a, pp’) at E, = 172 MeV. The experimental set-up is shown in fig. 1. Telescope 1 (Tl) was mounted on a turntable, whereas the telescopes 2, 3 and 4 (T2, T3, T4) were built up at fixed angles of 8 = 30’ with respect to the beam axis: T2 and T4 at opposite sides of the beam and T3 out of the reaction plane defined by Tl and the beam axis. Coincidences between one particle detected in Tl, which served as a trigger telescope, and a second particle detected in one of the other telescopes T2, T3 or T4 were measured. All the required AE, E and time signals were recorded event by

362

B. Ludewigt

et al. / Proton emission

“trigger-telescope”

“7ut

of

plane” beam

Fig. 1. Experimental set-up of the pp coincidence experiment.

event. The recording of the time signals corresponding to time differences within a time interval of several cyclotron periods allowed a determination of the accidental contribution to each particular kind of coincidence. The accidental background was in all cases smaller than 5 %. Three different two-particle correlations (Tl, T2), (Tl, T3) and (Tl, T4) were measured at the trigger telescope angles o1 = 20”, 50°, 65”.

3. Single-proton

spectra and the local excitation

model

The experimental single-proton spectra of the reaction 58Ni(a, p) and 19’Au(~, p) at E, = 100 MeV and E, = 172 MeV are shown in fig. 2. The spectra are averaged over 2-5 MeV depending on the statistics. The error bars represent the statistical errors only. The overall errors, due to uncertainties of the solid angles, the target thicknesses, the integrated beam current and the reaction losses, are estimated to be smaller than 20 % and 30 % for the 100 and 172 MeV data, respectively. The p-data shown in fig. 2 exhibit a spectrum shape and angular dependence corresponding to earlier measurements at E, = 140 MeV [ref. “)I. In fig. 2b the low energy peak of the spectra is due to evaporation from equilibrated compound nuclei or evaporation residues. At forward angles (0 < 40°) the spectra are expected to be dominated by direct reactions like projectile breakup in the nuclear field of the target 16). In the following the spectra at larger

B. Ludewigt et al. / Proton emission

0

30

60

90

50

363

100

150 EIMeV

Fig. 2. Inclusive proton spectra for ‘sNi target (a, b) and 19’Au target (c) and incident a-energies of 100 MeV (a) and 172 MeV (b,c) at different lab angles. The dots represent experimental data with error bars indicating the statistical error only. Full lines are the results of the local excitation model as explained in the text.

364

B. Ludewigt

et al. / Proton emission

angles, which are dominated by preequilibrium predictions of a simple reaction model.

reactions,

will be compared

to the

The preequilibrium part of the p-spectra can roughly be reproduced by assuming an isotropic emission from a source moving with a velocity intermediate between the velocities of the compound nucleus and the projectile I’). This feature suggests a model analogous to the fireball model used at relativistic energies ‘). A geometrical model is assumed to be appropriate since the de Broglie wavelength of the m-particle at the energies discussed here is small compared to the nuclear dimensions. For the model calculation the following assumptions have been made: The CIprojectile moving in a straight line towards the target interacts in the first step of the reaction only with the nucleons in the geometrical overlap volume. By this it creates a highly excited zone which is regarded as a ,system of nucleons decoupled from the remaining part of the target and emitting fast particles before, in the later stage of the reaction, the remaining energy dissipates throughout the whole nucleus. The size of the overlap volume and the number of the participating target nucleons N,(b) as a function of the impact parameter b are calculated as described in ref. 9). The total number of participating nucleons N(b) is obtained by adding to N,(b) the four nucleons of the c.+projectile. The maximum impact parameter is determined by the condition that more than two target nucleons must be involved. The velocity /3 of the hot zone, i.e. the mean velocity of the narticipating nucleons in beam direction and the internal energy E* are determined by energy and momentum conservation. The hot zone is regarded as a highly excited Fermi gas at temperature T which is related to E* by:

E*

_

N(b)7-2. K

(1)

K is theoretically not well established. Reasonable The level density parameter values range from 8 to 16 MeV. Assuming a Fermi gas energy distribution, the nucleons are able to overcome the nuclear attraction in the high energy tail of the distribution function. Because this part Maxwell-Boltzmann shape, the following is reasonable :

of the distribution has approximately a ansatz for the emission probability P(E)

P(E) - E*exp (-E/T),

(2)

where E is the proton energy in the rest frame of the hot zone. The energy spectra are transformed into the lab system and normalized to the integral cross section. The double differential cross section is obtained by summing up the contributions from all impact parameters, using the geometrical weight 2nb.

B. Ludewigt et al. 1 Proton emission

365

No weighting with N(b) was applied, contrary to the original fireball model ‘), since at the relatively low excitation energies discussed here, the nucleon multiplicity is generally of the order of 1 and therefore the emission probability is likely to be independent of the number of nucleons in the hot zone. The Coulomb interaction is further taken into account by including the slowing down of the projectile in the vicinity of the target nucleus and the repulsion of the emitted proton. The Coulomb energies used are 5.9 and 11.7 MeV for the system p+58Ni and p+ 19’Au, respectively. The level density parameter K was chosen to be 12 MeV yielding the best overall agreement with the experimental spectra. The results of the model calculations were normalized to the experimental data by adjusting an angle-independent normalization factor for each of the three reactions: N(s8Ni, E, = 100 MeV) = 0.33; N(58Ni, E, = 172 MeV) = 0.52; and N( 19’Au, E, = 172 MeV) = 0.2. Since the normalization factors represent the ratio of the integrated experimental p cross section to the geometrical cross section, N may be regarded as the average proton multiplicity. In fig. 2 the results of this model calculation are shown in comparison with the data. The preequilibrium parts of the experimental spectra are well described by the calculation. Especially the good reproduction of the angle dependence from 0 = 45” up to 8 = 130° should be noticed. In summary, the simplifications and assumptions underlying the presented model are: (i) The protons are assumed to be emitted from a hot zone, determined by a clean-cut geometry and decoupled from the residual part of the nucleus. (ii) By using straight-line geometry, the Coulomb deflection of the cr-projectile is neglected. (iii) The energy distribution is assumed to have Maxwell-Boltzmann shape with a temperature determined by eq. (1). (iv) The number of protons emitted per reaction is assumed to be independent of the impact parameter.

4. Analysis of the pp correlations Ratios of the measured pp coincidence yields, which make up a large, portion of the light particles coincidences, are listed in table 2. The interesting quantities C and C’ are defined as follows:

where 0 (out-of-plane correlation) and I (in-plane correlation) are the number of coincidences (Tl, T3) and (Tl, T4), respectively, and OR and IR are the inclusive

366

Li. Ludewigt et al. 1 Proton emission TABLE 2

pp coincidence Tl

yield ratios

(statistical

error

in brackets)

T2. T3, T4 c

(1,

c

Emi, - &,w

.%i, -Km,

(MeV)

(MeV)

(de&

I

13-31 13-31 t3-31

22-39 22-39 22-39

20 50 65

0.86 (9’:;,) 0.61 (10 ;$,) 0.66 (15 ‘X,)

0.73 (10 “‘,<,) 0.89 (14 “,,)

0.92 0.83 0.8

0.89 0.78 0.75

If

20-80 20-80 20-80

22-39 22-39 22-39

20 50 6’

0.79 ( 7 I’;,) 0.59 ( 4 I’,‘i) 0.56 (1 1 ‘I;)

_ 0.84 ( 6 I’,) 0.89 (10 :,<,)

0.9 0.78 0.74

0.83 0.66 0.63

III

13-20 13-20

12-18 10-15

20 50

1.0 (12 y,) 0.95 (14 :,,)

65

0.96 (16 ‘I,,)

CT-,,, (pi

Cm&

(;I

_ _

yields of T3 and T4. C’ is the analogous expression to C with T3 replaced by T2. The ratios C in group I and II are significantly smaller than 1 and therefore suggest a contribution to the cross section from a direct reaction. At 8, = 50” and W, i.e. at angular differences @i-8, close to 90” (the kinematical condition for free pp scattering), the out-of-plane to in-plane ratios C are si~i~~antly smaller than at 8, = 20”. This indicates a quasifree scattering component, which has been proved to be significant in relativistic heavy ion reactions ’ ** 19). If only protons (detected in T2, T3 or T4) with an energy smaller than 20 MeV are taken into account, the ratios C are about 1 at all angles 9i (see table 2), since in this energy region the uncorrelated compound or residual nucleus evaporation dominates. In fig. 3 three coincident p-spectra (Tl, T2), (Tl, T4), (Tl, T3) and the inclusive p-spectra, all measured with the trigger telescope Tl at 8, = 50” are shown. The shapes of the coincidence spectra (Tl, T3) and (Tl, T4) are very similar to the inclusive spectrum, but the coincidence cross section (Tl, T3) is about one-third smaller than (Tl, T4). The enhancement of the coincidences (Tl, T2) in comparison with (TI, T3) may be due to the break-up of the or-particle into four nucleons. This is suggested by the observation that the enhancement is maximum at E, = 35 MeV in approximate agreement with the mean energy of the projectile nucleons after break-up. The in-plane (Tl, T4) and out-of-plane (Tl, T3) anisotropies in the yield ratios (table 2) and in fig. 3’and 4 are discussed in terms of two different models. In the first one, the cross section of the emission of two protons is divided into two components : CT=@,-t-+.

(3)

B. Ludewigt et al. / Proton emission

367

x

x

.

IO3 Q+,

s

++e -

p-p-coin

-

l

0

*

q+

*

c=4

-

0

c=3

-

+

t2

20

0

LO

60

E,/MeV

Fig. 3. Experimental proton spectra at 0, = SO”: Inclusive spectrum and three pp coincidence spectra. The energy range of the coincident proton in telescope T2, T3, and T4, respectively, is 12-40 MeV.

100

Fig. 4. In-plane (Tl, T4) minus out-of-plane (Tl, T3) difference spectra at lab angles 200, 500, and 6S” of the trigger tetescope Tl. The experimental data (dots) (T1, T4)- (TL, T3) with error bars indicating the statistical error are compared to DKO calculations (full lines) and to the resuits of the local excitation model (dashed line). Both calculations are multiplied by an angle independent normalization factor.

368

B. L~de~igt

et al. / Proton emission

Here, the first term (2, represents the cross section for the emission of two protons by a quasifree scattering process (also called direct knock-out process (DKO)) of a target proton by a projectile proton. Provided that oR contains only uncorrelated pp emission, the in-plane to out-of-plane ,differences should be completely described by a 1. In the following the DKO term is treated as free pp scattering modified by the Fermi motion of the nucleons in the projectile and target nucleus. The parametrization of Chen et ai. 20) is used for the calculation of the pp cross section ap,(E), which is assumed to be isotropic in the pp rest frame. The momentum distribution of the nucleon inside the cr-nucleus is described by a gaussian 21):

9(~,) = exp(-P,~/P~J pa, = 140 MeV/c.

(4)

Since the quasifree pp scattering takes place preferably on the surface of the target nucleus, the momentum distribution of the surface nucleons has to be used instead of an average value. According to calculations of Durand et al. 22) this distribution can be approximated by a gaussian, too: S(PNi f = ev

(5)

( - Pki/Pii”h

where pNj is the nucleon momenturn and &i, = 150 MeV/c. The quasifree pp cross section as a function of the momenta p1 and p2 of the emitted protons is calculated by folding the free pp cross section with the momentum distributions of projectile and target:

d64wd dp,p,

x

=

* (PNiaPaoJ3 ss

~ppULll.~ B,.,,U~e~‘m’Ig(P,lg(P,i)

a3 T& t4~~-~:-~Z---s”i.~~i-~(3~,-~,)~f

+Q

>

dPdPa>

(61

where N is a normalization constant, t?“, is the scattering angle of proton 1 in the pp c.m. system, f‘(#;.“.) the cm.-lab transformation, pNi the proton momentum in the target nucleus before scattering, pa the proton momentum in the a-projectile before scattering, pB the projectile momentum per nucleon, p1 the momentum of proton 1 after scattering, pz the momentum of proton 2 after scattering and Q the 58Ni(a, pp’)60Ni Q-value. The &function takes care of the energy and momentum conservation. Eq. (6) has been evaluated by numerical integration over momentum intervals pl, pz and using an angle-independent normalization N. In fig. 4 the differences of the pspectra (Tl, T4)-(Tl, T3) resulting from this calculation are shown together with

B. Ludewigt et al. / Proton emission

369

the experimental data. The shape of the difference spectrum at 8, = 50° is well reproduced, whereas the agreement with the two other spectra is only fair. The splitting of the coincident cross section (3) into a DKO part and a remaining one allows a simple interpretation of the observed differences only if crR is strictly uncorrelated. But this assumption is true only in a limiting case, since even a statistical emission from a source containing a finite number of nucleons yields correlations due to energy and momentum conservation. Simple estimates of this effect have been made by Lynch et al. 23) assuming an isotropic thermal emission (Maxwell-Boltzmann distribution) from a source with temperature T containing A nucleons and moving with velocity o0 in the beam direction. In this case, the coincident cross section is proportional to the product of the cross section for the emission of proton 1 and the cross section of proton 2 from a source with (A - 1) nucleons and a changed temperature 7” and velocity ub and vice versa. For a first guess one may use the source parameters (A = 11, u0 = O.lc, T = 9.5 MeV) obtained by a “moving source Iit” to the experimental single p-spectra “). The resulting out-of-plane to in-plane yield ratios C (T-tit) are generally larger than the experimental ones (table 2). A better approximation is provided by calculating the parameters of the emitting source as a function of the impact parameter in terms of the geometrical model developed in sect. 3. The yield ratios C (model), as obtained by integration over impact parameter, experimental intervals and solid angles, are only slightly larger than the experimental C-values (table 2). Calculations of coincident proton spectra were performed to compare the local excitation model in more detail with the experimental correlation data. Although the shape of the coincident spectra (fig. 5) and of the difference spectra (fig. 4) is not well described, the general trend of the data is reproduced.

4. Summary and discussion Over a wide range of lab angles from about 40° to 145O the presented simple geometrical model is capable of describing the experimental inclusive proton spectra remarkably well. This local excitation model is expected to give correct results, provided the projectile momentum transferred to the (impact parameter dependent number of) participating nucleons is calculated properly and the phase space is occupied statistically. The phase space distribution can be a result of the experimental averaging over many reactions and all unmeasured observables or, indistinguishable from this case, can be the result of a local thermal equilibration. Appreciable differences between in-plane and out-of-plane correlations have been observed in pp coincidence measurements. In the local excitation model these differences can partly be explained by correlations caused by the finite number of participating nucleons. On the other hand, the observed correlations provide evidence for the presence of a direct knock-out component.

370

B. ~~e~igi

et at. 1 Proton emission

10 0

20

40

60 E, /MeV

Fig. 5. Proton-proton coincidence spectra (Tl,T4) and (Tl,T3) at 8, = 50°. Experimental data (dots) with error bars indicating the statistical error are compared to results of the local excitation model (dashed lines) normalized to the p,p3 coincident spectrum.

The findings suggest that, due to finite number effects, pp correlations are produced in a statistical reaction similar to a direct reaction and are becoming stronger with decreasing number of involved nucleons. Because of the smearing out by the nucleonic Fermi motion inside the colliding nuclei, the different components are difficult to distinguish and a more elaborate model is needed for quantitative estimations of their respective contributions. The Jtilich, Jiilich during

authors wish to thank the Institut fur Kernphysik, Kernforschungsanlage for the kind hospitality and their support during the experiments at the cyclotron. We also like to thank Dr. G. Gaul for his continuous support the accelerator runs.

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