Systematics of the nuclear giant dipole resonance

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A649 (1999) 193c-196c

Systematics of the Nuclear Giant Dipole Resonance Dimitri Kusnezov ~', Y. Alhassid ~ " and K.A.Snover b t "Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06520-8120, USA bNuclear Physics Laboratory, Box 354290, University of Washington, Seattle, WA 98195, USA We study the systematics of the giant dipole resonance width r in hot rotating nuclei as a function of temperature T, spin J and mass A. We compare available experimental results with theoretical calculations that include thermal shape fluctuations in nuclei ranging from A = 45 to A = 208. Using the appropriate scaled variables, we find a simple phenomenological function F(T, J, A) which approximates the global behavior of the giant dipole resonance width in the liquid drop model. We reanalyze recent experimental and theoretical results for the resonance width in Sn isotopes and 2°Spb. 1. I N T R O D U C T I O N Giant dipole resonances (GDR) are used as a probe of nuclei under extreme conditions of high temperature and spin [1,2]. The adiabatic fluctuation theory has been successful in describing the GDR observables (i.e. absorption cross-section and angular anisotropy) in hot rotating nuclei [3]. With this theory, one can compute the GDR cross-section using either Nilsson-Strutinsky (NS) or liquid drop (LD) free energy surfaces. We have performed a systematic analysis of experimental data from A = 45 to A = 208 using this theory [4]. Here we discuss one aspect of the study: the behavior of the GDR width F as a function of mass A, spin J and temperature T. 2. S C A L I N G P R O P E R T I E S

AND WIDTH PARAMETERIZATION

We have studied the systematics of the GDR width in both the LD and NS approaches. In the LD limit we obtain a phenomenological formula for F, while the NS approach is used to understand the importance of shell corrections. We start with an analysis of the spirt dependence in the LD model. In Fig. 1 we compare data for l°eSn [5] to our LD calculations (solid), and those of Ref. [5], which use a different LD parameterization. In Fig. 2, data for sg'6ZCu at various temperatures is shown and compared to theoretical curves calculated at three temperatures: T = 1.4 (lower), 1.8 (middle) and 2.2 (upper) MeV. The general LD behavior for nuclei in different mass regions is shown in Fig. 3(a). "This work was supported in part by DOE grant DE-FG02-91ER40608. tThis work was supported in part by DOE grant DE-FG-97ER41020. 0375-9474/99/$ see front matter © 1999 ElsevierScience B.V. All fights reserved. PII S0375-9474(99)00059-7

194c

D. Kusnezov et al./Nuclear Physics A649 (1999) 193c-196c

15

i

o 1.4-1.8

T = 1.8 l~eV

[] 1 . 8 - 2 . 2

/ o

//

I"

~

15

ii /

////

10

10

20

40 J (~)

5

60

Figure 1. Spin dependence of F in 1°8Sn [5], compared to our theory (solid) [4] and that of Ref. [5] (dashes).

i;;

sg,e3Cu !

0

2O

Figure 2. Spin dependence of r in sg'SSCu [6] for a variety of temperatures, compared to LD calculations at T = 1.4 (lower), 1.8 (solid) and 2.2 (upper) MeV.

In the high spin limit, the dominant spin dependence originates from the rotational energy J2/2I. Since I ,,, A s/s, one might expect that a spin scaling by A 5/e will remove the mass dependence in Fig. 3 (a). The ratio F(T, J, A)/F(T, J = O, A) is plotted as a function of ~ = J / A 5/6 in Fig. 3(b) (at T = 2 MeV), where evidence of scaling is apparent. This ratio depends on temperature (Fig. 3 (c)), and as a function of ~ is flatter at higher temperatures. It is possible to find an approximate power law which removes the T dependence of this ratio as well, as shown in Fig. 3 (d). The average behavior is represented by L(~) (solid), where L(~) - 1 ~ 1.8(1 + exp[(1.3 - ~)/0.2]) -1. For a complete parameterization of the width, we need to understand the systematics P(T, J = 0, A). At high temperatures F can be shown to increase with temperature as v ~ , but we find (in the LD limit) that log(1 + T/To) gives a better fit over a wider range of temperatures (the experimental systematics is shown in Figs. 4 and 6). We find r(T, J = 0, A) - to(A) + =(A)log [1 + ~], where To = 1 MeV is a reference temperature. We conclude that a good phenomenological formula to describe the global dependence of the LD GDR width on temperature, spin and mass is:

J, A) = r(T, S = O, A) [L \AS/S/j r(T, J = 0, A) = r0(A) + c(A) Iog0 + T/To).

(1)

to(A) is u s u r y extracted from the measured ground state GDR, and c(A) ~ 6.45-A/100 for the nuclei we studied. In Figs. 5 (a)-(b), we test Fs¢,led and L(~) against experiment

195c

D. Kusnezov et al./Nuclear Physics A649 (1999) 193c-196c

and find good agreement. Finally, in Fig. 6 we compare our results to n ° S n and 2°SPb data [7] and previous theoretical calculations. In the bottom row, we have reanalyzed the data and revised the temperatures. This is now more in line with fusion data (crosses) and our computations.

• " ~

-

u

. . . .

i

.

.

.

.

.

.

i

. . . .

i

. . . . .

b''" a

m

a

a

n

o

.

i

.

.

.

.

i

.

.

.

.

o *

I

25

50

(¢)1

...........

0.0

J (]I)

0.5

1.0

1.5

a)

J/A "/'

,

0.o

.

15

.

":":::

'°

.

0.5

*.0

~/A'/O

,.5

o.0

0.5

,.o

j/AS/,

,.5

0

.

.

i

1

.

.

.

.

i

2 T (U v)

.

.

.

3

Figure 3. (a) Behavior of F in LD model Figure 4. Temperature dependence of r in for selected nuclei. (b)-(c) Evidence of scal- sg'sscu for low spin [6] compared to theory ing at different T. (d) (F(T, J, A)/F(T, J = (solid) [4]. O,A))(z/%+s)/4 vs ~ for T = 1,2,3,4 MeV, and L(~) (solid).

3.

CONCLUSIONS

The systematics of the G D R width of hot rotating nuclei can be readily understood in terms of the adiabatic fluctuation theory. W e axe able to develop a phenomenological formula in the liquid drop limit that describes the global behavior of the the width as a function of mass, temperature and spin. REFERENCES

i. K.A. Snover, Ann, Rev. Nucl. Part. Sci. 36 (1986), 545. 2. J. Ga~rdhoje, Ann. Rev. Nucl. Part. Sci. 42 (1992), 483. 3. See for example, Y. Alhassid, in New Trends in Nuclear Collective Dynamics, p. 41, Y. Abe, H. Horiuchi and K. Matsuyanagi, eds., Springer Verlag, New York, 1992; Y. Alhassid, these proceedings; W.E. Ormand, these proceedings.

196c

D. Kusnezov et al./Nuclear Physics A649 (1999) 193c-196c

t * c u 'u"

0 / I

[

..agr"

~apb 10

+

o

10

~"~" 2O

rs~.,~ (MeV) O

t

^

"~aw~

0

>

~2

5 ¸

v

~spb

g~

lOi 5

g-"

0 O.0

0.5

1.0

J/A 5/6

Figure 5. Top: Comparison of experimental widths to the widths calculated from (1). Bottom: Testing experiment against the function L(~) (solid).

0

2

0 1 T (MeV)

2

Figure 6. Temperature dependence of F in x2°Sn and 2°SPb. Top: we compare experiment [7] to our NS (solid) and LD (dots) results [4], and to similar calculations of Ref. [7] (dashes and dot-dashes, respectively). Bottom: same comparison, but with revised data points and together with fusion d a t a (crosses).

4. D. Kusnezov, Y .ALhassid and K. Snorer, Phys. Rev. Lett. 81 (1998), 542. 5. M. Mattiuzzi et al, Nucl. Phys. A612 (1997), 262. 6. J.J. Gaardhoje et al, Phys. Rev. Lett. 53 (1984), 148; C.A. Gossett et al, Phys. Rev. Lett. 54 (1985), 1456; J. J. Gaardhoje et al, Phys. Rev. Leer. 56 (1986), 1783; M. Kicinska-Habior et al, Phys. Rev. C 36 (1987), 612; D.R: Chakrabarty et al, Phys. Rev. C 36 (1987), 1886; A Bracco et al, Phys. Rev. Left. 62 (1989), 2080; K.A. Shover, AIP Conf. Proc. 259 (1992), 299; M. Kicinska-Habior et al, Phys. Rev. C 45 (1992), 569; M. Kicinska-Habior et al, Phys. Lett. B 308 (1993), 225; J.P.S. van Schagen et ed, Phys. Lett. B 343 (1995), 64; A. Bracco et al, Phys. Rev. Left. 74 (1995), 3748; Z.M. Drebi et al, Phys. Rev. C 52 (1995), 578; ft. Butsch et al, Phys. Rev. C 41 (1990), 1530; D.R. Chakrabarty et al, Phys. Rev. C 53 (1996), 2739; E. Ramakrishnan et al., Phys. Rev. Lett. 76, 2025(1996): E. Ramakrishnan et al., Phys. Lett. B383, 252(1996). 7. W.E. Ormand, P.F. Bortignon, and R.A. Broglia, Phys. Rev. Lett. 77 (1996), 607; W.E. Ormand et al, Nucl. Phys. A 614 (1997), 217.