Quenching of photon decay in hot giant dipole resonances

Physics Letters B 320 (1994) 216-220 North-Holland

PHYSICS LETTERS B

Quenching of photon decay in hot giant dipole resonances A. S m e r z i a,b, M. D i T o r o a,b a n d D . M . B r i n k c a Dipartimento di Fisica dell" Universith di Catania, 57, Cor6o ltalia, 95129 Catania, Italy b INFN, Laboratorio Nazionale del Sud, Catania, Italy c Dipartimento di Fisica, Universitk di Trento, 38050 Povo (Trento), Italy

Received 4 June 1993; revised manuscript received 12 November 1993 Editor: G.F. Bertsch

The quenching of photon decays in giant dipole resonances (GDR) at high excitation energy (E*) is explained as due to the competition between y-ray and particle emission. This effect is related to a large increase of the GDR width with the temperature of the nucleus in presence of a pre-equilibrium mechanism that also tends to reduce the collective dipole strength. A saturation of the GDR width at high excitation energy cannot account for the experimental data. Limiting temperatures for the observation of GDR 7-decays are deduced. The E*-dependence of photon yields above the GDR region is also discussed.

There is considerable interest in the disappearance o f nuclear collectivity in compound nuclei at high excitation energy: it could provide information on new damping mechanisms and on the limits o f the existence o f hot nuclear systems. However quite controversial conclusions have been extracted from data on G D R photon emission in the high E*-region [ 1 - 6 ] . The main point is that the shape o f the experimental ~-ray spectrum can be equally well reproduced by using a G D R spreading width which either saturates or increases continuously with E" [5,6]. On the other hand there is some clear experimental evidence which deserves a thorough explanation and which can shed some light on the problem. It is a decrease o f the dipole strength in the giant resonance region at high excitation energies, with a consequent saturation of the number of emitted photons [ 2 - 6 ] . This observation has been recently associated with a pre-equilibrium mechanism [7,8]. Indeed if at high temperature the G D R states do not reach a statistical equilibrium with the c o m p o u n d nucleus before it cools down by neutron emission, the G D R states will not be populated and a smaller g a m m a emission strength will appear in the G D R energy region. However a strong increase of the G D R width, with a related smoothing o f the resonant form factor o f the 7-absorption cross section, also leads to a saturation 216

in the y-multiplicity. The increase in the G D R width would be due to nucleon-nucleon collisions that become more and more important in the damping o f the collective motion because of the Pauli-blocking suppression with increasing temperature. This effect has been studied in a semiclassical approach by solving the B o l t z m a n n - N o r d h e i m - V l a s o v equation [9-11 ]. There is a general agreement on the interpretation o f the observed saturation of the width: the nucleus cools down by neutron emission and the gamma rays which are detected originate from a nucleus with a lower excitation energy. The disagreement relies on the cooling mechanism. In refs. [5,6,11 ] neutrons are emitted from an equilibrated compound nucleus and the high energy photons are suppressed because o f a large increase in the G D R width. In ref. [8] particles are emitted before a full equilibration o f the compound system, i.e. before the G D R state can be statisticaUy populated. The point that we would like to stress in this letter is that such a pre-equilibrium effect seems to be not large enough to account for the experimentally observed quenching o f the G D R y-yield and a rapidly increasing G D R width is in any case necessary to account for the data. We make a quantitative analysis by considering the m a x i m u m possible reduction o f the G D R strength due to the pre-equilibrium effect. This is achieved just asElsevier Science B.V. SSDI 0370-2693 ( 9 3 ) E I 4 6 5 - A

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suming that at the time of compound nucleus formation (defined as t = 0 in the following) no G D R components are present in the system. As it will be discussed later this assumption is actually not fully justified in the medium beam energy region of interest here [12,13]. If we call Po (t) and P c ( t ) respectively the probabilities for the compound nuclei to exist with a G D R excitation and without, choosing as initial condition Po(t = O) = O a n d P c ( t = 0) = 1 we obtain [8,12] ), ;t+#

Pm(t) --

exp(--Tevt) {1 -- e x p [ - ( 2 + I t ) t ] } ,

2 - + - It exp(-yevt) P c ( t ) --- ;t x

("

7. + e x p [ - ( 2 +

It)t]

)

,

(1)

where It is the transition rate between compound states with the G D R built in and without, 2 is the inverse transition rate, with 2/It << 1 due to the different final state level densities, and 7ev is the transition rate of particle evaporation. We have a strong competition between the value of yev and It in order to reach the equilibrium. The probability for ?,-decay is given by

F

Pr =

dt~'r PD(t),

(2)

0

where ?r is the transition rate of photon emission. Finally the probability of photon emission integrated over the resonance region is / f2° M~v d E F~(E) F~ Pr"~J,2M~v F~v F~ + l"ev

(3)

where ~(E)-

E2 (rthc) 2 ar-abs(E) e - E / r ,

(4)

with 2NZ ar_a~(E) = (60 MeV mb) - 7tA

x

(_F'GDRE) 2 ( E 2 - E 2 D R )2 +

S /'GDR

(5)

(/-'GDRE) 2 '

and S, EGDR, F + = h i t , FGDR are respectively strength (in percent o f the EWSR), energy, spreading

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40, O) 5Z_

3C

212 r--C3

2C

05D (_9

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o

~oo

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Fig. I. Excitation energy dependence of the total ODR widths in Sn isotopes used in the Cascade analyses. The used evaporation widths are also reported (bottom points). The various curves are explained in the text. width and total width of the giant resonance (Full Width Half Maximum); F~v = hTcv is the energy integrated evaporation width. In our calculations we have used an accurate statistical evaluation of F~, [11 ], in good agreement with the emission widths obtained in [ 14,15 ]. The corresponding values are shown in fig. 1. Once we have the particle and photon decay widths we can compute, using a Monte Carlo technique, the actual number of neutrons, protons and photons emitted as a function of the initial excitation energy. We have performed the analysis for a Sn compound nucleus, where many data are presently available [ 16,16 ]. In fig. 1 we show the different E*-behaviours of the total G D R widths used in the calculation. The full line is a total excitation energy parametrization based on the theoretical evaluations of temperature dependence described in ref. [11 ], where effects of particle collisions and their interplay with the R P A widths are taken into account. The excitation energy is determined from a level density parameter a = A/IO, which consistently reproduces the particle emission rates, as shown later. A new improved simulation o f the collision term is used, suitably tested in exactly solvable cases [ 17 ]. The final values of the widths are nicely fitted by the c u r v e FODR = 4.8 + 0 . 0 0 2 6 . E *t'6 (MeV), which is just the high-E" extrapolation of low energy results [ 1-3 ]. We must remark that this result likely represents an upper limit to the increase in the width with excitation energy due to collisional 217

Volume 320, number 3,4 :oFT-'',

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PHYSICS LETTERS B

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Fig. 2. a) GDR photon emission yields yield as a function of the total excitation energy in Sn compound nuclei. The curves correspond to the different choices of FGDR(E*) shown in fig. 1. Experimental points from refs. [5,6]. b) The same for y-yields in the region 25 ~< E r ~< 40 MeV. damping. Two main corrections should both act in the direction o f reducing it: i) Surface effects from a smoothing density will imply larger mean free paths and so less collisions, particularly at higher temperatures, when we expect a further smearing o f the nuclear surface; ii) A free nucleon-nucleon cross section has been used: a decrease due to m e d i u m effects would also lead to larger relaxation times. The dashed line o f fig. 1 corresponds to a saturating G D R width, with a behaviour like the previous one for E* ~< 130 MeV and a constant value FODR = 11 MeV for E* > 130 MeV as suggested in ref. [ 18]. In this case the spreading width is not E*-dependent: the increase and the final saturation of the total F W H M is only due to angular m o m e n t u m effects [ 18,19 ]. In the same figure we plot also the used particle evaporation widths computed with two choices o f the level density parameter: a = A/IO (crosses), a = A/12 (circles). In fig. 2 we report the excitation energy dependence of photon multiplicities. Fig. 2a shows photon yields integrated in the G D R energy window (12 ~< Er ~< 218

13 January. 1994

20 MeV) in the Sn case. The calculation is performed with a simplified CASCADE code where only photon, neutron and proton emissions are considered. All the theoretical curves are normalized at the same point at low excitation energy. 5 × 105 events are considered in the Monte Carlo procedure. Data are from refs. [5,6], where the neutron emission has been also measured at each excitation energy. Data below E* "-- 150 MeV are from a different entrance channel (JAERI experiment in ref. [6] ) and so the emitting compound nuclei are not exactly the same for the whole E* range. Nevertheless we can have an idea o f the general trend o f the excitation function of the G D R 7-decay for A ~_ 120. We see that an increasing E*-behaviour o f the G D R width can reproduce the experimentally observed saturation o f the G D R photon emission at E* _~ 200 MeV [3,5,6,16]. We can get a corresponding limiting temperature for the G D R in Sn isotopes T _~ 4.0 MeV. The use of a constant spreading width (dashed line of fig. 2a) leads to a too large y-yield at high E*. Moreover the photon quenching is obtained only at excitation energies of about 400 MeV, corresponding to limiting temperatures T -~ 7-8 MeV, in disagreement with data. A larger Fev, which could be obtained with a level density parameter a = A~ 12 (see fig. 1 ), is not sensitively affecting this result, while the corresponding estimate for neutron emission will overshoot the data, as shown later. However since large uncertainties are present in statistical emission calculations at high E* (level densities, binding energies, opening o f new channels) we stress that the important region o f careful comparison with data should be in the range 200-300 MeV excitation energy. It has been recently observed that an increase o f FODR should affect the high energy part of the yspectrum [20]. In fig. 2b we plot photon yields integrated in a higher energy window (25 ~< Er ~< 40 MeV), abovc the G D R region. Now there is no saturation: the y-multiplicity is expected to increase with excitation energy, almost independently on the behaviour of the G D R width. The temperature effect, due to level densities, on the slope of the spectrum seems to dominate although the curve with increasing Foog (solid) appears systematically higher than the one for a constant width (dashed). This y-energy region is difficult to analyse experimentally because

Volume 320, number 3,4

2(

PHYSICS LETTERS B

" ' 1 . . . . I . . . . I . . . . I . . . . I"~ d

b-txl Z

5

'

;

,,c t,,,I

z

2.

....

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. . . .

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.... Ill

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-

03 C

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0,5 -oo

-

"100

200

300

400

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Fig. 3. Neutron and proton emission yields as a function of the total excitation energy in Sn compound nuclei. The solid lines are the results of our Monte Carlo analysis using the E*-increasing behaviour for the GDR width. Neutron data are from refs. [ 5,6 ] and circles show the result of an evaporation calculation performed by the authors within a full Cascade approach with their sharp E*-increasing parametrization of the GDR width.

o f the competition with the direct bremsstrahlung component [6,16 ]. Evaluation o f the latter just from extrapolation o f higher beam energy data is not trivial since the Pauli blocking for nucleon-nucleon collisions is playing a quite different role. To show that the statistical particle emission is correctly reproduced within our Monte Carlo approach, in fig. 3 we present the corresponding neutron and proton multiplicities, computed using the E*-increasing parametrization o f /'GDR- The normalization is the same as for the 7- decay. In this case we do not see any saturation effect. The neutron increasing rate with excitation energy is in a nice quantitative agreement with data [5,6]. We remark that the inclusion o f a larger preequilibrium emission, which seems to be quite underestimated in the higher E/A-beam experimental points [8], will actually improve the agreement in figs. 2, 3 between data and results obtained with an E*-increasing G D R width. Since in our picture the G D R limiting temperature derives from a competition with particle evaporation in hot c o m p o u n d nuclei, we would expect larger values for lighter nuclei. On the other h a n d the zero temperature widths are decreasing with mass number. A likely compensation between the two effects could lead to

13 January 1994

a Tlim "~ 4 MeV almost not dependent on the nuclear mass. A systematics in theory and experiments would be quite interesting. Our conclusion is that pre-equilibrium effects computed with realistic particle emission probabilities are not large enough to reproduce the quenching o f giant dipole photons observed at high excitation energy. In order to obtain the correct limiting temperatures for the G D R it is necessary to use a resonance spreading width which increases with E* (and in this case the pre-equilibrium effects are less important). A reduction o f the resonant form factor eq. (5) will be sufficient to enhance the cooling by particle emission, in agreement with experiments. This conclusion can be tested performing new experiments in a larger range o f masses and in an energy region just above the one o f saturation o f the angular m o m e n t u m of the compound nucleus. Finally we would like to stress that the initial conditions PD = 0, Pc = 1 which lead to the correction in eq. (3) are certainly overestimating such preequilibrium effects. Actually some dipole oscillations in the fused system are likely present due to the long equilibration time o f the charge degree o f freedom [ 12,13 ]. This is quite evident for N/Z-asymmetric entrance channels but it should be seen also for N/Zsymmetric partners particularly at the high energies o f interest here. Indeed N/Z-fluctuations due to preequilibrium emissions in incomplete fusion events will bring some isovector dipole strength in the fused system. More experimental work is certainly needed in this medium energy region, possibly also with radioactive beams in order to enhance the range of N/Z asymmetries.

We warmly thank Aldo Bonasera and Tiina Suomijarvi for many stimulating discussions.

References

[ 1 ] D.R. Chakrabarty et al., Phys. Rev. C 36 (1987) 1886. [2] A. Bracco et al., Phys. Rev. Lett. 62 (1989) 2080. [3] J.J. Gaardhoje et al., Phys. Rev. Lett. 59 (1987) 1409; Nucl. Phys. A 538 (1992) 573c. [4] G. Enders et al., Phys. Rev. Lett. 69 (1992) 249. [5] K. Yoshida et al., Phys. Lett. B 245 (1990) 7. [6] J. Kasagi et al., Nucl. Phys. A 538 (1992) 585c. [7] D.M. Brink, Nucl. Phys. A 519 (1990) 3c. 219

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[8] P.F. Bortignon, A. Bracco, D.M. Brink and R.A. Broglia, Phys. Rev. Lett. 67 (1991) 3360. [9] G.F. Burgio and M. Di Toro, Nucl. Phys. A 476 (1988) 189. [ 10] A. Bonasera, M. Di Toro and F. GulmineUi, Phys. Rev. C 42 (1990) 966. [ 11 ] A. Smerzi, A. Bonasera and M. Di Toro, Phys. Rev. C 44 (1991) 1713. [12] Ph. Chomaz, M. Di Toro and A. Smerzi, Nucl. Phys. A 563 (1993) 509. [13] Ph. Chomaz, Z. Jiquan, A. Smerzi and M. Di Toro, New pieces into the Hot Giant Dipole Resonance puzzle, Int. Winter Meeting on Nuclear Physics (Bormio, 1993) ed. I. loft, pp. 427-450. [14] V. Weisskopf, Phys. Rev. 52 (1937) 295; A. Friedman and G. Lynch, Phys. Rev. C 28 (1983) 16.

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[15] F. Pulhofer, Nucl. Phys. A 280 (1977) 267. [16] T. Suomijarvi et al., Study of hot Giant Dipole Resonance with the MEDEA detector, preprint Orsay IPNO DRE 92-35, in: Proc. INFN-RIKEN meeting on Perspectives in Heavy Ion Physics (SIF, Bologna, 1993), eds. M. Di Toro and E. Migneco, pp. 189-197. [17] A. Bonasera, M. Di Toro, A. Smerzi and D.M. Brink, Nucl. Phys. A 569 (1994) 215c. [18] F.V. De Blasio, W. Cassing, M. Tohyama, P.F. Bortignon and R.A. Broglia, Phys. Rev. Lett. 68 (1992) 1663. [19] P.F. Bortignon et al., Nucl. Phys. A 495 (1989) 155. [20] T. Suomijarvi, private communication; J.H. Le Faou et al., Towards limiting temperatures in nuclei: the behavior of collective motion, IPN-Orsay preprint Oct. 93