Pis’ma v ZhETF, vol. 118, iss. 10, pp. 721 - 722

Spreading widths of giant monopole resonance in the lead region:

Random matrix approach

N. N. Arsenyev⁺, A. P. Severyukhin^+∗, R. G. Nazmitdinov^+∗1)

⁺Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

^∗Dubna State University, 141982 Dubna, Russia

Submitted 3 October 2023

Resubmitted 13 October 2023

Accepted 17

October 2023

DOI: 10.31857/S1234567823220032, EDN: piipnj

The general idea on Giant Resonance (GR) decay

(QRPA) in very large two-quasiparticle spaces. To con-

properties as a consequence of the coupling of high-lying

struct wave functions of the excited 0⁺ states up to

modes with the lowest collective vibrational modes [1-4]

20 MeV we take into account all two-phonon terms that

requires further development in light of discussion on the

are built from the phonons of different multipolarities

role of order and disorder (chaos) in nuclei [5, 6]. We

λ^π = 0⁺, 1^-, 2⁺, 3^-, 4⁺, coupled to 0⁺ state (see de-

recall, however, that the analysis of spreading widths,

tails in [23, 17, 24]). Following the basic ideas of the

associated with the cascade of couplings and their frag-

quasiparticle-phonon model [4], the Hamiltonian is then

mentations due to these couplings (cf. [7-10]), is a real

diagonalized in a space spanned by states composed of

challenge for nuclear structure theory. Nowadays, most

one and two phonons coupled by means of the micro-

successful attempts in this direction are restricted by

scopic coupling matrix elements (see details in [20, 25]).

the consideration of the microscopic coupling between

In the item ii) the statistical description of the GMR

one-phonon and two-particle-two-hole (2p - 2h) or two-

fragmentation is based on ideas from the RMT [26, 27].

phonon configurations (see, e.g., discussion in [11-17]).

Namely, the one-phonon states are generated by means

In this paper we suggest the alternative approach,

of the QRPA calculations, while the coupling matrix el-

based on ideas of the Random Matrix Theory (RMT)

ements between the one-phonon and two-phonon states

[18, 19], which enables us to count effectively the prob-

are replaced by random matrix elements of the Gaus-

lem of the hierarchy at the description of spreading

sian Orthogonal Ensemble type. Within the framework

widths. To provide a detailed overview of our ap-

of our approach the two-phonon model space is decom-

proach we consider only spherical or near-spherical nu-

posed on two subspaces that are differently coupled to

clei around²⁰⁸Pb and focus our attention on the spread-

the QRPA states. On the larger energy scale the gross

ing width of Giant Monopole Resonances (GMRs). To

structure and structure effects of the GMRs are de-

demonstrate the validity of our approach we compare

fined; that includes the random coupling to surface vi-

the results of: i) the microscopic calculations, based on

brations of a few strongest coupling matrix elements.

the coupling between one-phonon and two-phonon con-

On the smaller energy scale there is the random cou-

figurations, so called phonon-phonon coupling (PPC);

pling to surface vibrations of a majority (small) matrix

ii) the random matrix approach based on the one-

elements. This coupling is particularly responsible for

phonon approximation; iii) available experimental data

the fine structure of the strength function in the energy

for^204,206,208Pb nuclei.

region around the GMR.

To carry out the item i) we employ the modern

To illustrate the quality of our approach, all numer-

development of the quasiparticle-phonon model, where

ical calculations have been done on the basis of the

the single-particle spectrum and the residual interac-

Skyrme forces SLy4 [28, 29]. Switching on the strong

tion are determined making use of the Skyrme inter-

as well as the week interactions, with the chosen values

action without any further adjustments [20]. By means

σ₁ = 600 keV and σ₂ = 30 keV, the RMT results are

of the finite rank separable approximation [21,22] for

in a quite good agreement with those of the PPC (see

the residual interaction we perform the calculations

Fig. 1). It is notable that the strength distribution of the

within the quasiparticle random phase approximation

GMR, obtained in this case, is rather close to the ex-

perimental distribution [30]. The remarkable agreement

¹⁾e-mail: rashid@theor.jinr.ru

between the results of the PPC and the RMT calcula-

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2023

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This is an excerpt of the article

“Spreading

24.

A. P. Severyukhin, S.

Åberg, N.N. Arsenyev,

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R. G. Nazmitdinov, and K. N. Pichugin, Phys. At.

region: Random matrix approach”. Full text of

Nucl. 79, 835 (2016).

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Письма в ЖЭТФ том 118 вып. 9 - 10

2023