A semiclassical perspective on nuclear chirality

doi:10.1007/s11467-023-1339-6

Front. Phys.

2024, Vol. 19

Issue (2) : 24301 https://doi.org/10.1007/s11467-023-1339-6

VIEW & PERSPECTIVE

A semiclassical perspective on nuclear chirality

Radu Budaca^1,²(

)

¹. “Horia Hulubei” National Institute for R&D in Physics and Nuclear Engineering, Str. Reactorului 30, RO- 077125, POB-MG6 Bucharest-Mǎgurele, Romania
². Academy of Romanian Scientists, Splaiul Independenţei 54, 050044, Bucharest, Romania

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Abstract

The application of the semiclassical description to a particle-core system with imbued chiral symmetry is presented. The classical features of the chiral geometry in atomic nuclei and the associated dynamics are investigated for various core deformations and single-particle alignments. Distinct dynamical characteristics are identified in specific angular momentum ranges, triaxiality and alignment conditions. Quantum observables will be extracted from the classical picture for a quantitative description of experimental data provided as numerical examples of the model’s performance.

Keywords chiral symmetry triaxial nuclei semiclassical description

Corresponding Author(s): Radu Budaca

Issue Date: 21 September 2023

Cite this article:

Radu Budaca. A semiclassical perspective on nuclear chirality[J]. Front. Phys. , 2024, 19(2): 24301.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1339-6
https://academic.hep.com.cn/fop/EN/Y2024/V19/I2/24301

Fig.1 Classical energy surfaces for

j = j ′ = 11 / 2

and

I = 10, 13, 16

values of total angular momentum, as a function of

φ

and the normalized chiral variable

x / I

, when

γ = 90 ∘

α = α ′ = 0

(first column),

γ = 90 ∘

α = α ′ = 10 ∘

(second column),

γ = 100 ∘

α = α ′ = 0 ∘

(third column), and

γ = 100 ∘

α = α ′ = 10 ∘

(last column). The single or double minima are indicated with crosses.

Fig.2 Evolution with angular momentum of the chiral coordinate for the classical energy minima in the absence (a) and presence of tilting (b). The corresponding dependence on angular momentum of the azimuth coordinate of the classical energy minima is shown in panel (c).

Fig.3 The evolution as a function of triaxiality

γ

of the separatrix between dynamical phases with one and two minima represented by the critical angular momentum

I c

for

j = j ′ = 11 / 2

with and without tilting.

Fig.4 Classical trajectories given as intersection of the surfaces corresponding to constants of motion in the space of classical angular momentum projections

{I 1, I 2, I 3}

in units of

I

. Trajectories are presented for

I = 10, 13, 16

in absence of tilting when

γ = 90 ∘

(first row) and

γ = 100 ∘

(second row), as well as for a

α = α ′ = 10 ∘

tilting when

γ = 90 ∘

(last row). The classical energy value is taken as the ground state eigenvalue for the corresponding spin taken form Refs. [38-40].

Fig.5 The chiral potential (first row), effective mass (second row), yrast state

s = 1

(third row) and excited state

s = 2

(fourth row) probability distribution defined by Eq. (4.8), are represented as a function of the normalized chiral variable

x / I

for a selection of

I

values, in the absence of titling (

α = α ′ = 0

) when

γ = 90 ∘

and

γ = 100 ∘

. The single-particle spins are

j = j ′ = 11 / 2

Fig.6 The chiral potential (first row), yrast state

s = 1

(second row) and excited state

s = 2

(third row) probability distribution defined by Eq. (4.8), are represented as a function of the normalized chiral variable

x / I

for a selection of

I

values, when

γ = 90 ∘

with

α = α ′ = 5 ∘

and

α = α ′ = 10 ∘

tilting. The single-particle spins are

j = j ′ = 11 / 2

Fig.7 Theoretical energy differences between the states of the partner bands (

s = 1

and

s = 2

) as a function of angular momentum for different tilting

α = α ′ = 0 ∘, 1 ∘, 3 ∘

of the quasiparticle spins when triaxiality is

γ = 90 ∘

and

γ = 100 ∘

Nucl.	$j$ (hole)	$j ′$ (particle)	$α$	$α ′$	$E 0$ (MeV)	$J 0$ (MeV⁻¹)	$C$ (keV)	$r m s$ (keV)
¹¹⁹I	$92$ ( $π$ )	$112$ ( $ν$ )	3°	10°	2.293	29.294	0.19	61.4
¹³⁴Pr	$112$ ( $ν$ )	$112$ ( $π$ )	3°	3°	1.759	48.076	3.24	43.9
¹³⁸Pm	$112$ ( $ν$ )	$112$ ( $π$ )	0°	8°	2.303	35.681	3.34	31.4

Tab.1 The quasiparticle spins with the alignment angles

α

and

α ′

are listed together with parameters

J 0

(MeV⁻¹),

E 0

(MeV), and

C

(keV) obtained by fitting the experimental excitation energies of ¹¹⁸I [51], ¹³⁴Pr [9,52], and ¹³⁸Pm [53]. The fitting performance is ascertained by the

r m s

values given in the last column.

Fig.8 Comparison between experimental and theoretical energies of the partner bands (top), and the corresponding energy differences (bottom) for ¹¹⁸I [51], ¹³⁴Pr [9,52] and ¹³⁸Pm [53] as functions of total angular momentum. Only data points with filled symbols where included in the fitting procedure.

Fig.9 Comparison between experimental and theoretical

B (M 1) / B (E 2)

values for bands 1 and 2 of ¹³⁴Pr (a) [52] and ¹³⁸Pm (b) [53].

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