能量转移公式：可靠预测反应与捕获概率

132 浏览量更新于2024-09-04 收藏 309KB PDF 举报

"这篇学术文章‘能量转移公式可产生可靠的反应和捕获概率’发表在Physics Letters B739 (2014) 348–351期，作者包括A. Diaz-Torres, G. G. Adamian, V. V. Sargsyan和N. V. Antonenko。文章探讨了一种能量转移公式，该公式在预测重离子碰撞中的反应和捕获概率时表现出高度可靠性，尤其在系统质量增加和/或质量不对称性降低的情况下。" 在核物理和相关领域的研究中，理解和预测反应和捕获概率是至关重要的。本文提出的能量转移公式为这一领域提供了一个新的工具，它能够避免在低能量条件下进行复杂的反应计算，这在实际操作中可能是不切实际或难以实现的。通过比较该公式的预测结果与耦合通道计算（Coupled Channels Calculations）的结果，研究者发现，随着系统质量的增大以及重离子碰撞中质量不对称性的减小，公式的预测准确度显著提高。耦合通道计算是一种广泛使用的理论方法，用于处理原子核的多通道反应过程，包括弹性散射、捕获、裂变等。这种方法考虑了不同量子态之间的相互作用，但计算复杂度随系统复杂性的增加而增加。相比之下，能量转移公式提供了一个相对简洁的替代方案，能够在某些情况下提供可靠的结果。文章指出，这种能量转移公式在处理大型核系统或低质量不对称碰撞时特别有效，这可能是因为在这些条件下，系统的动态行为更易于用简单的能量转移模型来描述。此外，该公式对于实验数据的解释和未探索反应机制的理解也具有潜在价值，因为它可以提供一个快速估算反应概率的方法，而无需进行详尽的量子力学计算。这项工作强调了在核物理研究中开发和应用简化计算方法的重要性，特别是在处理大型和复杂系统时。能量转移公式不仅提高了计算效率，而且在一定程度上保证了预测的准确性，为核反应的研究提供了新的途径。在未来的研究中，这种公式可能被进一步优化和扩展，以适应更广泛的核物理问题。

Physics Letters B 739 (2014) 348–351

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Energy-shifting formulae yield reliable reaction and capture

probabilities

A. Diaz-Torres

a,∗

, G.G. Adamian

, V.V. Sargsyan

b,c

, N.V. Antonenko

European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT

∗

), Strada delle Tabarelle 286, I-38123 Villazzano, Trento, Italy

Joint Institute for Nuclear Research, 141980 Dubna, Russia

Yerevan State University, M. Manougian 1, 0025, Yerevan, Armenia

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

Article history:

Received

29 September 2014

Received

in revised form 5 November 2014

Accepted

6 November 2014

Available

online 8 November 2014

Editor:

J.-P. Blaizot

Predictions of energy-shifting formulae for partial reaction and capture probabilities are compared with

coupled channels calculations. The quality of the agreement notably improves with increasing mass of

the system and/or decreasing mass asymmetry in the heavy-ion collision. The formulae are reliable and

useful for circumventing impracticable reaction calculations at low energies.

(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP

1. Introduction

The physics of low-energy nuclear reactions is critical for un-

derstanding

energy production and nucleosynthesis in the uni-

verse [1].

The heavy-ion collisions at energies near the Coulomb

barrier are highly affected by the interplay of nuclear structure and

reaction dynamics [2–4], the bare Coulomb barrier being modiﬁed

by couplings and centrifugal effects. Coupled-reaction-channels

(crc) calculations provide partial, transmission and reﬂection co-

eﬃcients

that determine a number of reaction observables such

as capture and reaction cross sections. Although feasible nowadays

within various implementations [5,6], the crc calculations can be

sometimes computationally demanding and time consuming [7],

so a simple formula for the partial transmission and reﬂection co-

eﬃcients

seems to be useful. The energy-shifting formula has a

long history across disciplines [8,9]. The present paper addresses

the quality of energy-shifting formulae for partial reaction and

capture probabilities at near-barrier energies. We ﬁrst present the

energy-shifting formulae and a description of the crc calculations,

followed by results and a summary.

2. Energy-shifting formulae

The key idea of the energy-shifting formula [8–10] consists

in replacing the exact, reaction and capture probabilities for a

nonzero partial wave J and a given incident energy E, P

reac

(E, J)

and P

cap

(E, J), with the corresponding s-wave probabilities evalu-

ated

at a lower energy:

Corresponding author.

E-mail

address: torres@ectstar.eu (A. Diaz-Torres).

(E, J ) ≈ P

(

, J = 0), (1)

where i ={reac, cap} and 

= E − E

rot

( J ), E

rot

( J ) being inter-

preted

as a rotational energy. In the present paper, E

rot

( J ) is cal-

culated

in two different ways:

(i) The

ﬁrst way relies on expanding the Coulomb barrier height,

( J ), up to second order in Λ = J( J + 1), and subtracting

the

s-wave potential barrier, V

(0), so the rotational energy

reads as [8]:

rot

( J) =

2μR

2μ

, (2)

where μ denotes the reduced mass of the projectile–target ra-

dial

motion, R

and ω

are the radius and curvature of the

s-wave barrier, respectively. Using the lowest order in Eq. (2),

an energy-shifting formula has been used for deriving the

well-known Wong formula [11,12]. The second order correc-

tion

term in Eq. (2) takes into account the dependence of the

barrier radius on the angular momentum.

(ii) The

second way is based on a nuclear-modiﬁed Rutherford tra-

jectory

for the near-barrier projectile–target orbit [13], E

rot

( J )

being identiﬁed as the rotational energy at the distance of

closest approach:

rot

( J) = E

(η

2

+ J

)

1/2

− η



(η

2

+ J

)

1/2

+ η



, (3)

where η



= Z





μ/2

E is an effective Sommerfeld parameter

that takes into consideration the nuclear part of the nucleus–

nucleus

interaction potential through Z



= Z

(1 − a

)

http://dx.doi.org/10.1016/j.physletb.2014.11.007

0370-2693/

SCOAP

下载后可阅读完整内容，剩余3页未读，立即下载

weixin_38632247

粉丝: 8
资源: 1000

能量转移公式：可靠预测反应与捕获概率

PWM波的产生和捕获

接收机处理曲线（ROC），检测概率，虚警概率

gps 产生 捕获 代码

tms320f28027 设置了ECAP，已经知道捕获值，如何知道捕获时间差和计算捕获频率

ip 和 tcp 数据分组的捕获和解析

、在 GNSS 信号捕获中为了提升捕获性能的可靠性，所采用的多次试验(multi-trial)检测 一般有 2 种执行方式：

关于gps信号产生 捕获跟踪 比特同步 帧同步 仿真程序

tms320f28027 设置了ECAP，已经知道捕获值，如何计算捕获频率

pmf捕获verilog

最新资源

gps 产生捕获代码

、在 GNSS 信号捕获中为了提升捕获性能的可靠性，所采用的多次试验(multi-trial)检测一般有 2 种执行方式：

关于gps信号产生捕获跟踪比特同步帧同步仿真程序