裂变集体惯性比较：非微扰方法与GCM分析

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"这篇研究文章探讨了裂变过程中的非扰动集体惯性，并通过比较分析，揭示了这种非微扰方法在计算核裂变路径上的集体惯性时的优越性和适用性。研究中，作者使用了Adiabatic Time Dependent Hartree Fock Bogoliubov (ATDHFB)理论，并在高斯重叠近似(GOA)框架下将其扩展到生成器坐标法(GCM)，特别关注了密度依赖力的影响。通过对$^{234}$U的裂变路径进行计算，发现非扰动方案预测的集体惯性与扰动计算相比，不仅结构更丰富，而且表现出更强的一致性，接近于精确的GCM惯性。这些发现为裂变的微观描述提供了新的稳定基础，表明非扰动惯性可以作为一个有效的工具，只需加入一个经验性因子即可模拟精确的GCM结果。" 这篇在《Physics Letters B》上发表的研究文章，重点关注了核物理领域中的裂变过程，特别是集体惯性的计算方法。集体惯性是理解裂变动力学的关键参数，因为它描述了核在裂变过程中克服势能壁垒的能力。传统的扰动方法可能无法充分捕捉到核结构的复杂性，而本文提出的非扰动方法ATDHFB-GCM在高斯重叠近似下的应用，展示了对核结构的更准确捕捉。作者Samuel A. Giuliani和Luis M. Robledo等人分别来自美国密歇根州立大学的NSCL/FRIB实验室、西班牙马德里理工大学的计算模拟中心以及马德里自治大学的理论物理学系。他们在文章中详细阐述了计算过程，包括非扰动方法的扩展、应用和比较。关键词包括裂变、集体惯性、生成器坐标法以及Adiabatic Time Dependent Hartree Fock Bogoliubov理论，这些关键词揭示了研究的核心内容和技术手段。文章经过多次修改和审阅，最终于2018年10月25日在线发表，编辑为W. Haxton。这项工作对理解和模拟核裂变过程具有重要意义，为未来更深入的核物理研究提供了新的理论工具和方法。

Physics Letters B 787 (2018) 134–140

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Non-perturbative collective inertias for ﬁssion: A comparative study

Samuel A. Giuliani

, Luis M. Robledo

b,c,∗

NSCL/FRIB Laboratory, Michigan State University, East Lansing, MI 48824, USA

Center for Computational Simulation, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain

Departamento de Física Teórica, Universidad Autónoma de Madrid, 28049 Madrid, Spain

a r t i c l e i n f o a b s t r a c t

Article history:

Received

26 July 2018

Received

in revised form 14 September

2018

Accepted

23 October 2018

Available

online 25 October 2018

Editor:

W. Haxton

Keywords:

Fission

Collective

inertias

Generator

coordinate method

Adiabatic

time dependent Hartree Fock

Bogolyubov

The non-perturbative method to compute Adiabatic Time Dependent Hartree Fock Bogoliubov (ATDHFB)

collective inertias is extended to the Generator Coordinate Method (GCM) in the Gaussian overlap

approximation (GOA) including the case of density dependent forces. The two inertias schemes are

computed along the ﬁssion path of the

234

U and compared with the perturbative results. We ﬁnd that the

non-perturbative schemes predict very similar collective inertias with a much richer structure than the

one predicted by perturbative calculations. Moreover, the non-perturbative inertias show an extraordinary

similitude with the exact GCM inertias computed numerically from the energy overlap. These results

indicate that the non-perturbative inertias provide the right structure as a function of the collective

variable and only a phenomenological factor is required to mock up the exact GCM inertia, bringing new

soundness to the microscopic description of ﬁssion.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Despite its discovery dates back almost 80 years, ﬁssion still re-

mains

a major challenge for nuclear theory [1]. The lack of a feasi-

ble

full quantum formalism describing the evolution of the nucleus

from the ground state to scission enforces the adoption of differ-

ent

approximations, which in turn provide a theoretical framework

for the estimation of ﬁssion properties in nuclei. For instance, the

starting point in any traditional energy density functional calcula-

tion

is the original assumption that ﬁssion can be described using

a reduced set of collective variables [2,3]. Within this approxima-

tion

the ﬁssion probability is obtained as the probability of the

nucleus to tunnel under the ﬁssion barrier, which is driven by the

potential energy surface (PES) and the collective inertias felt by

the nucleus in its way to scission [4,5]. Both quantities, together

with the collective ground-state energy, enter in the collective ac-

tion

integral allowing for the calculation of the spontaneous ﬁssion

lifetime by means of the semiclassical Wentzel–Kramers–Brillouin

(WKB) approach.

sound calculation of the PES, collective ground-state en-

ergy

and collective inertias is thus essential for a proper estima-

Corresponding author.

E-mail

addresses: giuliani@nscl.msu.edu (S.A. Giuliani), luis.robledo@uam.es

(L.M. Robledo).

tion of ﬁssion lifetimes [1,6]. If the formalism that shall be used

in the calculation of the ﬁrst two quantities is well established,

the same cannot be claimed for the collective inertias. Nowadays

two theoretical frameworks allow for a derivation of a collective

Schrödinger equation and its associated inertia: the Adiabatic Time

Dependent Hartree Fock Bogoliubov (ATDHFB) formalism and the

Generator Coordinate Method (GCM) with the Gaussian overlap ap-

proximation

(GOA) [1]. In both approaches the collective inertias

can be written in terms of the collective momentum operators,

which in turn can be related to the linear response matrix (LRM)

and its inverse when acting on Hartree Fock Bogoliubov (HFB)

wave functions. Given the whopping number of two-quasiparticle

elementary excitations in realistic applications to ﬁssion, the di-

mensionality

of the LRM is very high and therefore its inverse is

diﬃcult to evaluate. To avoid this bottleneck the assumption of

diagonal dominance of the LRM is often used, leading to the tra-

ditional

perturbative cranking formulas for the collective inertias

involving denominators composed of two quasiparticle energies.

Abetter approximation to the exact expression of the collective

inertias was introduced in [7](see also [8]), where the collective

momentum operator is computed in terms of the derivatives of

the density and pairing tensor with respect of the collective vari-

ables.

This non-perturbative cranking calculation of the collective

inertias, implemented in the ATDHFB approach, showed that the

numerical treatment of the derivatives gives rise to a less adiabatic

https://doi.org/10.1016/j.physletb.2018.10.045

0370-2693/

SCOAP

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