Testing the level density of A ∼ 100 hot nuclei from evaporative charged-particle spectra

ELSEVIER

Nuclear Physics A578 (1994) 285-299

NUCLEAR PHYSICS A

Testing the level density of A - 100 hot nuclei from evaporative charged-particle spectra G. Nebbia a, D. Fabris a, A. Perin a, G. Viesti a, F. Gramegna b, G. Ptete b, L. Fiore c, V. Paticchio 'I, F. Lucatelli d, B. Chambon e, B. Cheynis e, D. Drain e, A. Giorni f, A. Lleres f, J.B. Viano f a

d

Istituto Nazionale di Fisica Nucleate and Dipartirnento di Fisica deU'Universitd di Padova, I-35131 Padova, Italy b Laboratori Naziorali di Legnaro, I-35020 Legnaro (Padova), Italy Istituto Naziorale di Fisica Nucleare, Sezione di Bad, I-70126 Bari, Italy Istituto Naziorale di Fisica Nucleate and Dipartintento di Fisica deU'Universitô di Firenze, I-50125 Firenze, Italy e Institut de Physique Nucleaire, F-69622 Vrlleurbanne Cedex, France f Institut de Sciences Nucleaires, F-38026 Grenoble Cedex, France Received 11 January 1994; revised 6 April 1994

Abstract Alpha particles and protons emitted in the 32 S + 74 Ge reaction at E =160, 210, 259, 335 and 435 MeV were measured in coincidence with evaporation residues. The average inverse level-density parameter for hot evaporation residues with A - 100 was obtained by comparing the slope of the charged-particle spectra with the predictions from a full statistical model calculation . Spectral shapes are well reproduced by calculations using the standard values < K ) = 7.5 MeV, except for alpha particles at the highest bombarding energy, which corresponds to an excitation energy E = 2.2 MeV/nucleon. The present results are compared with other experimenial investigations in the A - 100 and A -160 regions and with predictions from theoretical models. Difficulties in extracting the nuclear temperature from the slope of the particle spectra for A - 100 are discussed.

?~ words: NUCLEAR REACTIONS 74Ge( 32 S,

aX); E =160, 210, 259, 335, 435 MeV; measured light-charged-particle multiplicity M., light-charged-particle (residues) coincidences ; deduced nuclear-level density

1. Introduction One of the most challenging problems in the study of the decay of atomic nuclei at high temperature and angular momentum consists in the description of the 0375-9474/94/$07.00 C 1994 Elsevier Science B.V . All rights reserved SSDI 0375-9474(94)00242

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phase space available to the system and its structural modifications as the excitation energy of the nucleus increases. For this purpose it is important to know the density of nuclear levels p that the decaying nucleus can populate as a function of the excitation energy E*. The Fermi-gas prescription has usually been adopted to describe the nuclearlevel density at low excitation energies [1], p(E*) =

0.13 go expr2 ( 6W2goE*

)1/21

* )sl4

(goE where g o is the single-particle level density at the Fermi energy and E* is the nuclear excitation energy . Introducing the nuclear temperature T as the inverse logarithmic derivative of the level density one has

1 1/2, Ir 2go 1 dp _ -5_ _ p dE* 4E* + ( 6E* where 6ir 2 go = a is called the "level-density parameter" . Evaluation of a for uniform Fermi gas yields a - A 1vIeV -1 . It is well known that this value underestimates the density of levels at energies slightly above the Fermi energy, one reason being that the calculation is performed for bulk particle densities neglecting the diffuseness of the actual nuclear potential which implies a large effective nuclear volume for the particles near the top of the Fermi distribution. A host of experimental data [2] shows that the so-called inverse level-density parameter K =A /a - 8 describes the level density at moderate excitation energy throughout the chart of the nuclides. On the other hand there is well-documented experimental evidence that the value of K approaches the Fermi-gas value as the excitation energy increases. Such transition :.as been found in nuclei of mass A - 160 [3-5], where charged-particle spectral slopes and multiplicities were used to extract the initial nuclear temperature T of the emitting systems. There has been extensive theoretical discussion on the implications of the variation of the level density with excitation energy. Several calculations employing t%vc-body formalism yield a decrease of a with excitation energy since within these models the nucleon effective mass decreases with temperature [f-8]. Recently Shlomo and Natowitz [9] performed a calculation including pairing and shell effects, continuum states and in particular the effect of the finite size of the nucleus which reflects on the frequency dependence of the effective mass (correlations with the surface degrees of freedom) and consequently on the calculation of a for different nuclear masses. Such calculations have been ca"ried out for a wide range of nuclei at various temperatures showing that the transition energy from the low excitation-energy value (K - 8 Meal) towards the Fermi-gas value (K - 15 MeV) depends on the nuclear mass. It is therefore interesting to extend the study of the level density in highly excited nuclei in mass regions different than A - 160 where the relevant body of

1 T

G. Nebbia et al. /Nudear Physics A578 (1994) 285-299

287

experimental data was obtained both in incomplete- [4] and complete-fusion experiments [5]. In tl~e neighboring A =100-120 region, studies of the level densities at high excitation energies yielded contradictory results [10]. Furthermore, the existing data in this mass region are the result only of incomplete fusion reactions hi which a variety of nuclei are formed with a wide range of temperatures and angular momenta, making the knowledge of the initial conditions of the decaying nucei rather uncertain. This prompted a further investigation of the level density in the mass region A 100, using complete (or nearly complete) fusion reactions and covering carefully the excitation-energy span in which the transition is expected on the basis of theoretical predictions.

2. Experimental details The experiment was performed using 32 S beam energies of 160 and 210 MeV at the XTU Tandem accelerator of the Laboratori Nazionali di Legnaro and of 259, 335, 435 MeV at the SARA coupled cyclotrons facility of the Institut des Sciences Nticleaires in Grenoble . Targets consisted of 280 1Lg/cm 2, 95% enriched 74Ge evaporated onto a 20 wg/cm2 12C backing . The relevant parameters of the five reactions studied are reported in Table 1. The evaporation-residue cross sections are deduced from the Bass model [11] and the critical angular momenta for fusion-evaporatior~ residues are evaluated accordingly. A. wide-angle electrostatic separator was used to measure evaporation residues close to the be--im axis, rejecting both the primary beam and the elastic-scattering events. The separator, basically a plane capacitor, was 50 cm long and was operated at 15 kV/cm. The entrance collimator allowed to select a slice of the kinemat cal cone around the beam axis from Blab = 0° to about Blab = 10°,thus covering basically all of the evaporation-residue angular distribution. The evaporation residues (ER) were detected in a set of three 7-strip silicon counters 300 pm thick, with a total surface of 18 x 4 cm2 , placed on a movable arm 117 cm downstream from the target position after the electrostatic separator. Table. 1 Ebeam (MeV)

160 210 259 335 435 a

E* (MeV) 100 136 170 223 292 a

Fractional momentum transfer 0.93% .

a,ER (mb) 1200 960 790 600 510

JÉR

67 69 69 69 69

G. Nebbia et aL /Nuclear Physics A578 (1994) 285-299

288 1-1105

32S+'"Ge Et.,è =160 MeV

w 103 b 102

10

10

4 0 1 L 30 Ecm ( MeV Fig. 1. (a)-(g) Center-of-mass spectra of protons and alpha particles detected at various laboratory angles for the five bombarding energies . Solid, dotted and d(-dashed lines are the results of calculations performed with the statistical model code CASCADE using respectively < K > = 7.5, 10, 12. 10

20

Identification of the ER's was performed by measuring their energy and time-offlight. Light charged particles (LP) were detected in a set of five quadruple telescopes in which the first three elements were silicon surface7-~')arrier detectors of 20, 200, 2000 pm thickness, backed by a 1 cm long CsI(Tl) crystal. The telescopes were placed at Blab = 30°, 50°, 70° and 130° on the side of the beam axis opposite to the ER's, and one at elab = 50° on the same side. The fast signal of any one of the telescopes that fired was used as a time-reference pulse for the ER time-of-flight measurement . Evaporation-residue singles were also collected measuring the time-of-flight with the pulsed beam. Samples of the measured proton and alpha-particle spectra are shown in Fig. 1 . The light charged-particle spectra of Fig. 1 have been fit by a surface-evaporation function, [(E - B )/(Tapp)2 ] exp[ - (E -- B)/ Tapp ], where E is the particle kinetic energy_, Tapp is the apparent temperature and B is the emission barrier. In this function Tapp represents the slope of the high-energy side of the evaporatedparticle spectra and is generally thought of aE the average temperature of the emitting source along the entire de-excitation cascade . Furthermore the average multiplicity M was extracted from the experimental data by integrating the experimental differential multiplicities measured at the

G. Nebbia et al. /Nuclear Physics A578 (1994) 285-299

32 S+Tt Ge Età=2l0 MeV protons

C 10 3

w

3 r

b

N

10

2

10

._

i .

i

4G MeV

3

0

Fig. l (continued).

10

20

30 40 50 Ecm ( MeV )

different angles with the help of the Monte Carlo version (CACARIZO) of the CASCADE statistical model calculations described in the next paragraph. In the Monte Carlo simulation the effective experimental geometry (electrostatic deflector, ER detector, LP telescopes) was properly taken into account . Tapp and M values are reported in Table 2. During the SARA experiment, some of the first thin elements of the l.p. telescopes became noisy, introducing a high cut in the proton spectra. For this reason the extracted proton multiplicities at 335 and 435 MeV bombarding energies were affected by large uncertainties atA are not reported in Table 2. In order to improve the statistics, and consequently the fit quality, for the three highest energies, the spectra collected at different baexward angles were transformed in the center-of-mass system and then summed together ; in these cases only the two telescopes at 70° and 130° were used in order to avoid a possible contribution to the particle spectra from pre-equilibrium emission at forward angles that might be present as the bombarding energy increases. From systematics of linear momentum transfer in heavy-ion collisions [121 we can assume complete fusion of projectile and target for the four lowest energies, while a fractional momentum transfer of PLMT = 0.93 Js deduced for the reaction at 435 MeV. Accordingly the excitation energy of the compound nucleus in this last case was estimated using the relation [41 ECN

-

mt

mr + mp/PLNrr

E~ab + Q

G. Nebbia et al. INuclear Physics A578 (1994) 285-299

290

Fig. I (continued).

and represents the average excitation energy of the incomplete-fusion nucleus associated to the most probable momentum transfer PLMT* A measurement of the ER velocity at the highest bombarding energy yields a value of momentum transfer of about 92% of the full momentum transfer, in good agreement with the predictions from systematics quoted above. The assumed excitation energies E* are reported in Table 1. In Table 2 are also listed the average thermal e-.-citation energy per nucleon E of the nuclei populated by alpha and proton decay, obtained by correcting E* for the average energy dissipated in the decay process and the rotational contribution . 3. Results

In previous works in the A - 160 region [4], the initial temperature at a given excitation energy E2 has been obtained by unfolding the measured apparent temperatures (Tapp,l , Tapp,2) at excitation energies Ei and E2 (E2 >El*) with the corresponding multiplicities Ml and M2 : T, =

M2 Tapp,2 - M I Tapp, I M2 -

MI

The assumption made here is that the particle cascade originating at Ei describes well the lower part of the de-excitation chain also whey it originates at

G. Nebbia et aL /Nuclear Physics A578 (1994) 285-2W "=s+''ce E,,,=4» MeV

291

-

C:10 3 w -v

Fig. 1(continued).

energy E2. Once T was determined, the inverse level-density parameter K was obtained simply by the relation K = T2/E. Applying the same analysis to the present data, unrealistically high T values (of the order of 4-5 MeV), which would imply very large K values; are obtained for both proton and alpha particles still at low excitaac-i energies kcorresponding to the two lowest boriharding energies), where level-density parameters of the order of a - sA are expected to describe the nuclear properties. In the effort of clarifying this result rather unexpected, the particle spectra have been compared with the predictions of CASCADE statistical model calculations [131 in which different average inverse level-density parameters were employed in the range < K > = 7.5-12 . It is important to note that in those calculations

Table Ebeam

160 210 259 335 435

(MeV)

E

a

0.4 0.8 1.1 1.6 2.2

(MeV/nucl .)

T.«pp (MeV)

2.5±0.1 3.2±0.2 3.7±0.2 4.5±0.2 5.3±0.2

M. 0.72±0.07 0.80±0.12 1.16±0.12 1.12±0.28 1.44±0.43

Tpp (MeV) 2.3±0.1 2.8±0.1 3.3±0.2 3.6±0.2 4.2±0.2

MP 1 .2±0.2 1.5±0.2 2.0±0.2

a Average thermal excitation energy per nucleon of the a- and p-decay daughters of the primary compound nucleus.

292

G. Nebbia et al. /Nuclear PhysicsA578 (1994) 285-299

the level-density parameter is assumed to be constant throughout the de-excitation cascade, so that the effective < K > value needed to describe a given particle spectrum has to be considered as the result of the integration of K(e) de weighted on the corresponding multiplicity M(e) for the emission of the particle at the excitation energy e. This means that the < K ) value is a good estimate of the actual value of the inverse level-density parameter K at the nominal compound-nucleus excitation energy only for those particles emitted preferentially in the earlier stages of the de-excitation cascade . Input parameters for the CASCADE calculations are those employed in the past in the A - 100 region and include optical-model (OM)-derived transmission coefficients [14,15]_ The ER critical angular-momentum values of Table 1 were used, without including fission competition. It was checked that calculated spectra are not sensitive to slight changes in the limiting angular momenta (as, for example, using the experimental data reported in Ref. [16] for the system 1013-225 MeV 32S +'6 Ge) or to the explicit inclusion of the fission competition . The shape of the calculated alpha-particle and proton spectra are compared with the experimental ones in Fig. 1. It is evident that the high-energy portion of the experimental spectra are generally well reproduced by the calculation with < K > = 7.5 MeV. We note that the low-energy part of the spectra shows a marked disagreement with the predicted distribution for protons as well as for alpha particles at the two lowest bombarding energies . The low-energy portion of the spectra is generally very sensitive to the emission barrier as defined by the transmission coefficients. It is well known that OM-derived tran:mission coefficients often need to be adjusted, defining empirically lowered barriers, in order to describe well the experimental spectra at low particle energies [15]. The CASCADE statistical model calculation is also predicting too large charged-particle multiplicities by about a factor 1.7 for alpha particles and 1.4 for protons. As far as the high-energy portion of the spectrum is concerned, it can be seen that the relatirely small difference in the calculated spectra requires a X2 analysis in order to determine the value of that best fits the data. The alpha-particle spectrum seems to indicate a need for a larger < K ) value only at the highest bombarding energy, where minimization of X2 calls for a value of < K ) = 9 as an input in the calculation. At variance with this result, there is no variation of the average inverse level-density parameter < K ) for protons. The different behaviour between protons and alpha particles can be qualitatively interpreted as reflecting the emission characteristics of the different particles. Following the predictions of the statistical model for A - 100 nuclei, protons are emitted with rather equal probability at any step of the de-excitation cascade while alpha particles originate preferentially at the top of the cascade . This difference between alpha particles and protons was experimentally demonstrated in the A - 160 region where it was shown that the apparent temperature of alpha particles is very close to the initial temperature, that of protons being much lower [5].

G. Nebbia et al. /Nuclear PhysicsA578 (1994) 285-299

This emission characteristic reflects also on the level-density parameter value extracted by analyzing the particle spectra . In the A - 160 case, the average level-density parameter values (i.e. the ) obtained by comparing the experimental with the statistical-model-predicted alpha-particle spectra were very close to the K values obtained by unfolding apparent temperatures T with the measured multiplicity M, which are supposed to be associated to the initial excitation energy. This demonstrates experimentally that in case of particles which are emitted preferentially at the top of the cascade, the comparison with statistical model cakulations using the average level-density parameter yields a lower limit for the actual luvel density at the nominal excitation energy, but not far from that value. Furthermore we note that the observations concerning the proton spectra are in good agreement with results reported in Ref. [171 concerning neutron emission from a compound system in the same mass and energy region. In fact for the A - 109 compound system at 326 MeV excitation energy, the neutron spectrum was very well reproduced by CASCADE calculations using the average level-density parameter a = gA . 4. Discussion From the results described in the previous section it is clear that the two methods of extracting information on the level density from the evaporated-particle spectra yielded contradictory results in the present case, at odds with the results obtained in the A - 160 region. Furthermore, a slight disagreement is verified with the results of Ref. [10] (in the overlapping excitation-energy region) where inverse level-density parameters K - 10-11 were extracted analyzing the slope of the proton spectra with the help of statistical model calculations . In that work, this inverse level-density parameter was determined for excitation energies in the range 158-405 MeV for nuclei with A =106-121 populated by the incomplete fusion reaction of 701 MeV 28Si + 1®°Mo. Correction factors f. were used, derived from PACER statistical model calculations, to correlate the proton-spectral apparent temperature Tapp with the initial temperature Tin ;, = f. Tapp used to determine the inverse level-density parameter by using the relation K = Ti2 it/E

To test the possible role of statistical model codes in producing the above discrepancies, calculations for the 32S on 74Ge reactions were also performed by using the PACE2 code, a preliminary version of PACER. Results are shown in Fig. 2 comparing the shape of experimental particle spectra with those predicted by PACE2 in which a level-density parameter a =A/7.5 is used . Generally the spectra are well described by calculations with standard level-density parameters as in the CASCADE case. It is therefore verified that different statistical model

294

G. Nebbia et ai. /Nuclear Physics A578 (1994) 285-299

6

C 10

ô 105 Cr`

4

10

Nb 010 3 102 10

Fig. 2. Comparison between the shape of the measured proton (a) and alpha-particle (b) spectra and predictions forom the PACE2 statistical model calculations . See text for details .

codes are able to reproduce the spectral shapes of the emitted particles with equally good accuracy and thus are not responsible for the discr;,pancy in the extracted value of K. The procedure described in Ref. [101, although in principle correct in order to deduce the slope of the "first-chance" particle spectra, assumes in using the relation K = T,nit /e that the slope of the particle spectra at a given excitation energy is, also in the A - 100 region, uniquely determined by the level density of the system . This relation should be used carefully also in case of first-chance emission . In fact it considers the phase space of the decaying nucleus being described by one dimension only, the excitation energy . Furthermore a single type of particle is emitted in the decay with sharp cutoff transmission coefficients . As a result, all effects related to the angular momentum, the competition between different decay channels and the transmission coefficients are neglected. It is experimentally demonstrated that there are some types of decay and/or of mass regions in which the above simplifications are not so important as it seems the case in the mass region A - 160. In order to check on this point for the mass region of interest in the present work, we have first looked back to our raw data, comparing with those from Refs. [10,181.

G. Nebbia et al. lNuclear Physics A578 (1994) 2 ..85-299 8 7 -

6

8

" uS +"Ge

N

protons

6'°0+Ag

V =OSi+' °° MO

o'S+Ag

4

5

0

`i

a o. 1--

7

6

e' =S+"Ge ®' s0+Ag

®'Si + "MO o'S+Ag

5

4

4 -

3

3

2

2%

97

*

2 4 5 3 1 2 3 4 5 E ( MeV/nucl ) E ( MeV/nucl ) Fig. 3. Apparent temperatures deduced from proton (a) and a:pha-particle (b) spectral slopes as a function of excitation energy per nucleon. Closed circles are from this work, open circles and squares are from Ref. [18), triangles are from Ref. [10). 1

2

Systematics of Tapp for the mass region A - 100--110 are reported in Fig. 3. It appears that the experimental data for protons and alpha particles are in reasonable agreement over the energy range considered, taking into account the existing slight differences in emitter mass. In Fig. 4 the experimental multiplicities of alpha particles are shoves. It seems here that two different regimes are separated : for excitation energies E < 2 MeV/nucleon it is Ma - 1, roughly independent from E . As the excitation energy increases, Ma starts growing almost linearly with E . A statistical model calculation shows qualitatively the same trend . The interpretation is that in this mass region the alpha-particle emission at low excitation energy is strongly determined by the angular momentum dependence of the phase space. Thermal effects (i.e. the influence of the excitation-energy degree of freedom in the alpha-particle emission) seem to take over only at E > 2 MeV/nucleon. This point suggests that the relation between nuclear temperature T and slope of the particle spectra should be considered very carefully for A - 100 at excitation energies E < 2 MeV/nucleon, as the bulk of the emission seems to be determined by the angular-momentum dependence of the phase space, at least in the case of alpha particles . As a second step, we have performed a simple test. We considered the particle spectra produced by the statistical model CASCADE for the 32S on 746e reactions by using the inverse level-density parameter Kin = 7.5 and determined their slope parameter Tapp with maxwellian fits. The Tapp values were in turn used to extract an apparent inverse level-density parameter KO.t by using the relation K u, =A Pp/Ef.c. where Ef, was the excitation energy corresponding to the first chance emission. We would expect Kout < 7.5 because the apparent temperature was associated with the excitation energy at the top of the cascade. Results are reported in Fig. 5 . The derived Kout., are very large in case of alpha particles,

29 6

G. Nebbia et al. f Nuclear Physics A578 (1994) 285-299 ô

4. 3.5 3. 2.5 2. 1 .5 1. 0.5 1

2

3 E

(

4

5

MeV/nucl )

Fig. 4. Alpha-particle multiplicities as a function of excitation energy per nucleon of the compound nucleus. The symbols are the same as Fig. 2. The 32 S+ 64 Ni data are from Ref. [15] . The solid line shows predictions from PACE2 statistical model calculations normalized to the experimental data .

demonstrating that for A -100 nuclei the spectral shape of the evaporated a particles is rather strongly affected by the so-called "spin-off" energy contribution [181, i.e. the angular-momentum-dependent contribution to the particle energy. More strikingly in our opinion, it is Kot > 7.5 also for protons . This demonstrates that the slope of the spectra is hardened by effects different from the pure nuclear temperature, also in case of nucleon emission from A - 100 nuclei. It is not simple to determine quantitatively the con¢nbutions to the proton-spectral slope different from the nuclear temperature T. Angular-momentum effects are expected to scale with the reduced mass of the system nucleus plus particle, being smaller in case of nucleons with respect to the alpha-particle case, as is qualitatively shown by the Kin/Kout test . A second and up to now completely neglected contribution might originate from the transmission-coefficient effects. It is well known that optical-model Tl,s for nucleons reflect the quantal origin of those particles and are characterized by the fact that they will never saturate to T, =1 . On the contrary the T,,s for heavier H isotopes and for 4 He are of semiclassical origin reaching the values T, = 1 at energies less than twice the barrier energy. This means that for - nuelfons -the change of the T, value mi ht in principle affect the high-energy slope of tl ee energy spectra . In base of A - 100 nuclei it is verified that this is indeed the case for proton-transmission coefficients as shown fin Ref. [15]. Therefore, it seems that the direct comparison with the statistical model is one possible way to extract information about the level density in the A - 100 region at low excitation energy (E < 2 MeV/nucleon). Model predictions give a sufficiently good account of the spectral slope for protons as well as for alpha particles, demonstrating that "spin-off" effects are

G. Nebbia et at. /Nuclear Physics A578 (1994) 285-299

297

17.5 F-

10. 7.s s.

2.s

.4

X

1.2

1 :6

20

2.4

28

E ( McV/nucl ) Fig. 5. Values of the parameter K., deduced from statistical model calculations at various excitation energies of the mass A =106 compound nucleus . The solid line refers to the K; parameter. See text for details.

correctly handled by the calculation . Furthermore from Table 1 one can notice that the values of the maximum compound-nucleus angular momentum associated with the ER decay channel remain constant over the bombarding energies investigated because of the fission cbannei . This gives us confidence that angularmomentum effects (both in formation and decay of tine compound nucleus) on the particle spectra should not change s~grificantly, as increasing the bombarding energy . As a result the discrepancies detected at the higher bombarding energy between the experimental alpha spectrum and the standard calculation using < K ) = 7.5 have to be attributed to a variation of the level_ density, the only other relevant parameter in determining the slope of the evaporative spectrum. 5. Conclusions

We hav :: uetermined the average inverse level-density parameter < K > for hot evaporation residues with A - 100 populated in the 32 S + 74 Ge reaction ., by comparing the slope of the charged-particle spectra with the predictions from a full statistical model calculation . This procedure has been used also in the work of Ref. [4] for the mass region A - 160 where a variation of the average value was detectable from the alpha-particle spectra as the excitation energy exceeded the value E > 1.5 MeV/nucleon . In the present experiment we do not detect any sizeable variation except for alpha particles at the highest bombarding energy, which correspond to E = 2.2 MeV/nucleon, suggesting that the value of K at the top of the cascade sh3ws very little change over the energy region investigated .

298

G. Nebbia et al. I Nuclear Physics A578 (1994) 285-299

The proton spectra seem to be also rather insensitive to changes of the level density at the top of the cascade, because the experimental spectra are strongly fed by particles emitted at lower excitation energies along the cascade. Furthermore it was verified i tat in the A -100 region, the slope of the particle spec;rum is determined not only by the nuclear temperature T, but also by other effects (angular momentum, transmission coefficients, etc.), so that it cannot be used directly to determine the level-density parameter by using the relation K=T2 /E, even when corrections for the cascade length (i.e. by factors fw in Ref. [10]) are used. These effects, if not property considered, yield an overestimate of the slope parameter determined from the particle spectra ; moreover, since their effect varies depending on the particle type, they lead to different values of K deduced from protons or heavier particles . Considering only the alpha-particle data which are supposed to be more sensitive to the excitation energy at the top of the cascade, the values of (K> deduced from this work are plotted in Fig. 6 together with the results from Wada et al. [18]. In that work K values were determined by unfolding alpha-particle spectral slopes with multiplicities, taking into account spin-off effects on the particle spectra. Apparently, our data on the inverse level-density parameter connect rather well with previous results obtained at higher energy and seem to indicate that a transition toward the Fermi-gas value a - SA exists in the mass A - 100 region at about 2 MeV/nucleon excitation energy . This excitation enerm, is substantially larger than that in the A - 160 case, in qualitative agreement with the model predictions of Ref. [9].

14 Y

12 10 8 6

E ( MeV/nucl Fig. 6. Values of ( K) deduced from the fits to the experimental particle spectra (filled circles). Squares and open circles are the K values determined in Ref. [18] for a system in the same mass region.

G. Nebbia et al. /Nuclear Physics A578 (1994) 285-29 9

2"

We thank the accelerator crews of the XTU Tandem in Legnaro and the SARA facility in Grenoble for providing good beam quality and efficient operation during the energy changes. We also want to thank Professor J.B. Natowitz for the fruitful discussions on the results presented in this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

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