The present study unfolds the relative importance of <math altimg='si1.svg'><mi>N</mi><mo stretchy='false'>/</mo><mi>Z</mi></math>, shell effects, and thermal fluctuations in shaping the temperature dependence of the isovector giant dipole resonance (IVGDR) width. To this end, we measured the <italic>&#947;</italic>-ray spectra from excited <math altimg='si2.svg'><mmultiscripts><mrow><mi mathvariant='normal'>Zn</mi></mrow><mprescripts /><none /><mrow><mn>62</mn><mo>,</mo><mn>68</mn></mrow></mmultiscripts></math> populated through 4He <math altimg='si3.svg'><msup><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow><mrow><mn>58</mn><mo>,</mo><mn>64</mn></mrow></msup></math>Ni reactions at beam energies of 28 MeV and 40 MeV, and compared the corresponding IVGDR widths with those for nuclei close to the doubly magic 56Ni and moderately away from it. The large-area modular BaF <inf>2</inf> detector array was used to detect high-energy <italic>&#947;</italic> rays ( <math altimg='si4.svg'><msub><mrow><mi>E</mi></mrow><mrow><mi>&#947;</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&gt;</mo><mn>4</mn></math> MeV). The Bayesian inference approach was combined with the statistical model analysis to extract the IVGDR parameters from the measured spectra. Calculation of IVGDR widths was performed using various theoretical approaches, specifically the thermal shape fluctuation model (TSFM) with microscopic energy density functional inputs. TSFM calculation was also performed using the free energy surfaces from the deformed liquid drop model. For 68Zn, the width is observed to increase closely following the TSFM prediction. In contrast, suppression of the width is noticed for 62Zn at low temperatures, similar to other nearby nuclei with <italic>N</italic> and/or <italic>Z</italic> closer to 28. Moreover, 68Zn indicates an early onset of the saturation in the IVGDR width, mimicking structural changes appropriately comprehended by the microscopic calculations. These findings suggest that the relative influence of microscopic effects and thermal broadening in the IVGDR width is strongly governed by the proximity of the decaying nucleus to magicity.

India

Chandrani Sen

Debasish Mondal

Gourab Banerjee

S. Mukhopadhyay

Jhilam Sadhukhan

Deepak Pandit

Surajit Pal

Sujan Kumar Roy

Balaram Dey

Srijit Bhattacharya

A. De

Pratap Roy

T.K. Rana

Rajkumar Santra

Saumanti Sadhukhan

Study of the giant dipole resonance around the magic number 28

The radiative decay of the Hoyle state serves as the gateway to the production of heavier elements in a stellar environment. Here, we present an exclusive measurement of electric quadruple (E2) transitions of the Hoyle state to the ground state of $^{12}$C through the $^{12}$C(p, p′γγ)$^{12}$C reaction. A triple coincidence measurement yields the radiative branching ratio <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>r</mi><mi>a</mi><mi>d</mi></mrow></msub></math>/Γ = 4.01 (30) × 10$^{−4}$. This result was corroborated by an independent experiment based on the complete kinematical measurement via $^{12}$C(p, p′)$^{12}$C reaction, yielding a consistent result of <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>r</mi><mi>a</mi><mi>d</mi></mrow></msub></math>/Γ = 4.04 (30) × 10$^{−4}$. Combining our results with the currently adopted values of <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>(</mo><mi>E</mi><mn>0</mn><mo>)</mo><mo>/</mo><mi>Γ</mi></math> and <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>(</mo><mi>E</mi><mn>0</mn><mo>)</mo></math>, the radiative width of the Hoyle state is determined to be 3.75 (40) × 10$^{−3}$ eV. It is important to note that our finding do not align with a recently reported 34% increase in the radiative decay width of the Hoyle state but is consistent with the currently accepted value.

S. Manna

Samir Kundu

K. Banerjee

A. Sen

R. Pandey

G. Mukherjee

T.K. Ghosh

S.S. Nayak

R. Shil

P. Karmakar

K. Atreya

K. Rani

D. Paul

R. Santra

A. Sultana

S. Basu

S. Pal

S. Sadhukhan

P. Pant

Sk M. Ali

S. Mondal

R. Datta

S. Bhattacharya

C. Bhattacharya

New measurement of the Hoyle state radiative transition width

The present paper investigates the impact of pairing correlation on the nuclear level density (NLD) and radiative strength function (RSF) of an odd-odd and rare-earth $^{166}$Ho nucleus. By employing the exact thermal pairing (EP) solution in conjunction with both the temperature-dependent independent-particle model (EP+IPM) for the NLD and the phonon damping model (EP+PDM) for the RSF, we achieve good agreement with the experimental NLD and RSF data, which have been recently extracted by using the Oslo method. Notably, without adding any extra parameters, our calculations successfully reproduce the pygmy dipole resonances (PDR) and a portion of the strength around the region of scissor resonance (SR) in the RSF. This suggests that the SR in this nucleus may be less pronounced than that obtained in the previous analysis within the phenomenological model. These features are the consequences of the EP and the couplings of the PDM phonon to all the particle-hole (ph), particle-particle (pp), and hole-hole (hh) configurations within the EP+PDM, thus insisting on the importance of the underlying physics involved in this model. Utilizing the obtained NLD and RSF, we predict the $^{165}$Ho<math><msup><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>γ</mi><mo>)</mo></mrow><mrow><mn>166</mn></mrow></msup></math>Ho and Maxwellian-averaged cross sections, which exhibit remarkable agreement with all the available experimental data from the Experimental Nuclear Reaction Data and Karlsruhe Astrophysical Database of Nucleosynthesis in Stars. These results reflect the imprint of the pairing correlation on those quantities.

Vietnam

Le Tan Phuc

Tran Vu Dong

Japan

Nguyen Dinh Dang

Bui Minh Hue

Le Thi Quynh Huong

Nguyen Ngoc Anh

Nguyen Quang Hung

Imprint of pairing correlation in (n, ) and Maxwellian-averaged cross sections of an odd-odd Ho nucleus

The collective rotational enhancement in the nuclear level density (NLD) arising due to nuclear deformation is still not well understood due to sparse experimental findings. To address this issue, angular momentum (J) gated neutron, proton and GDR γ-ray spectra have been measured from two deformed nuclei ($^{169}$Tm and $^{185}$Re) and one near spherical nucleus ($^{201}$Tl) by populating them around 26 MeV excitation energy. An enhanced yield compared to statistical decay is observed in all the three spectra (p, n, γ) for both the deformed nuclei but only statistical decay for near spherical nucleus. Intriguingly, the relative enhancement factors determined independently from all the spectra are very similar (≈10) for both the deformed nuclei. Moreover, the results indicate that the fadeout of the collective enhancement does not dependent strongly on the nuclear ground state deformation which is in stark contrast to the expectations of the phenomenological as well as microscopic calculations. The possible reasons for this discrepancy are discussed.

A.K. Sikdar

S.R. Banerjee

Puzzle of collective enhancement in the nuclear level density

The entropy excess caused by one proton (proton entropy excess) has been extracted for several pairs of medium and heavy mass nuclei such as ($^{237}$U and $^{238}$Np), ($^{231}$Th and $^{232}$Pa), ($^{211}$Po and $^{212}$At), ($^{196}$Pt and $^{197}$Au), and ($^{90}$Y and $^{91}$Zr) using the available nuclear level density data. The nature of entropy excess as a function of excitation energy <math><msup><mrow><mi>E</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> is found in a reasonable agreement with the microscopic calculations based on the exact pairing plus independent-particle model at finite temperature (EP+IPM). It is observed that the proton entropy excess is <math><mo>∼</mo><mn>0.1</mn><mo>−</mo><mn>0.5</mn><mspace width="0.25em"></mspace><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub></math> for the spherical systems and <math><mo>∼</mo><mn>1.0</mn><mo>−</mo><mn>1.2</mn><mspace width="0.25em"></mspace><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub></math> for the deformed ones, which is notably smaller than that of neutron entropy excess (<math><mo>∼</mo><mn>1.3</mn><mo>−</mo><mn>2.0</mn><mspace width="0.25em"></mspace><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub></math>). This is due to the effect of Coulomb interaction as well as the single-particle level density of protons, which is less than that of neutrons. Moreover, a peak-like structure in the entropy excess observed at low <math><msup><mrow><mi>E</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>&lt;</mo><mn>1</mn></math> MeV is possibly associated with the pairing reentrance phenomenon caused by the weakening of blocking effect in odd nuclei at low temperature within the EP+IPM. However, this peak-like structure, which is more pronounced in the spherical nuclei than in the deformed isotopes, is not well supported by experimental observation due to strong fluctuations of the measured data. Hence, further experimental and theoretical studies are called in order to understand this effect.

N. Dinh Dang

N. Ngoc Anh

L. Tan Phuc

N. Quang Hung

Proton entropy excess and possible signature of pairing reentrance in hot nuclei

Evaporated α-spectra have been measured in coincidence with low energy discrete γ-rays from residual nucleus $^{68}$Zn populated by αn evaporation from compound nucleus $^{73}$Ge produced in the reaction $^{64}$Ni($^{9}$Be,αn)$^{68}$Zn at <math><mi>E</mi><mo>(</mo><msup><mrow></mrow><mrow><mn>9</mn></mrow></msup></math>Be) = 30 MeV. Low energy γ-gated α-particle spectra, for the first time, have been used to extract the nuclear level density (NLD) for the intermediate $^{69}$Zn nucleus in the excitation energy range of E ≈ 4-20 MeV. The slope of present NLD data as a function of excitation energy for $^{69}$Zn matches nicely with the slope determined from RIPL estimates for NLD at low energies and the NLD from neutron resonance data at neutron separation energy <math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math>. The extracted inverse NLD parameter (k = A/<math><mover><mrow><mi>a</mi></mrow><mrow><mo>˜</mo></mrow></mover></math>) has been used to determine the nuclear level density parameter value a at neutron separation energy <math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math> for $^{69}$Zn. The cross section of $^{68}$Zn(n,γ) capture reaction as a function of neutron energy is then estimated employing the derived <math><mi>a</mi><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math> in the reaction code TALYS. It is found that the estimated neutron capture cross section agrees well with the available experimental data without any normalization. The present result indicates that experimentally derived nuclear level density parameter can constrain the statistical model description of astrophysical capture cross section and optimize the uncertainties associated with astrophysical reaction rate.

Subinit Roy

Md.S.R. Laskar

R. Palit

H. Pai

S. Rajbanshi

Sajad Ali

Saikat Bhattacharjee

F.S. Babra

Anjali Mukherjee

S. Jadhav

Balaji S. Naidu

Abraham T. Vazhappilly

Sanjoy Pal

Nuclear level density of Zn from gamma gated particle spectrum and its implication on Zn(n, ) Zn capture cross section

We examine the thermodynamic properties of mass <math><mi>A</mi><mo>∼</mo><mn>200</mn></math> nuclei utilizing angular momentum (J) gated nuclear level densities (NLDs) extracted in the excitation energy range of 2–15 MeV. Interestingly, the experimental NLDs are in good agreement with the results of a microscopic approach, which is derived based on the exact pairing plus the independent-particle model at finite temperature (<math><mrow><mi>EP</mi></mrow><mo>+</mo><mrow><mi>IPM</mi></mrow></math>), whereas the conventional Hartree–Fock BCS (HFBCS) and Hartree–Fock–Bogoliubov plus combinatorial method (HFBC) fail to describe these data. Consequently, the thermodynamic properties of those nuclei at finite angular momentum have been extracted using the <math><mrow><mi>EP</mi></mrow><mo>+</mo><mrow><mi>IPM</mi></mrow></math> NLDs. While the heat capacities of $^{200}$Tl, $^{211}$Po and $^{212}$At (near spherical nuclei) follow the trend as expected in odd–odd and even–odd masses, surprisingly an S-shaped heat capacity is found in odd–odd deformed nucleus $^{184}$Re. It has been shown that this S-shaped heat capacity observed in $^{184}$Re is caused by not only the breaking of nucleon Cooper pairs but also the change of pairing induced by deformation.

L.T. Quynh Huong

-shaped Heat Capacity in an Odd–odd Deformed Nucleus

An exclusive systematic study of the giant dipole resonance (GDR) parameters has been performed in very light mass nucleus <math><mmultiscripts><mrow><mtext>P</mtext></mrow><mprescripts></mprescripts><none></none><mrow><mn>31</mn></mrow></mmultiscripts></math> in the temperature range of <math><mo>∼</mo><mn>0.8</mn><mtext>–</mtext><mn>2.1</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math> and average angular momentum of <math><mo>∼</mo><mn>11</mn><mtext>–</mtext><mn>16</mn><mspace width="0.25em"></mspace><mi>ħ</mi></math>. The high-energy γ rays from the decay of the GDR, evaporated neutrons and γ-ray multiplicities have been measured. The angular distribution of high-energy γ rays has also been measured at <math><msub><mrow><mi>E</mi></mrow><mrow><mi>beam</mi></mrow></msub><mo>=</mo><mn>42</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>. The GDR parameters, nuclear level density parameter and nuclear temperature were precisely determined by simultaneous statistical model analysis of high-energy γ ray and evaporated neutron spectra. It is observed that the measured width remains roughly constant up to a temperature of <math><mo>∼</mo><mn>1.6</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>. Moreover, the thermal pairing plays no role in describing the GDR width in this open-shell light nucleus at the above-mentioned temperatures and angular momenta. The present measurements provide an excellent platform to extend the applicability of the existing theoretical models down to the very light mass nuclei.

Soumik Bhattacharya

S. Bhattacharyya

Study of giant dipole resonance in hot rotating light mass nucleus P

Exclusive measurement of isospin (I) mixing in $^{32}$S at high temperature (T) has been performed utilizing the γ-decay of isovector giant dipole resonance (IVGDR). The degree of isospin mixing was deduced from the ratio of high energy γ-ray cross-sections of $^{32}$S and $^{31}$P populated at the same temperature and angular momentum (J). Precise temperature was determined by simultaneous measurement of nuclear level density (NLD) parameter and angular momentum. The measured Coulomb spreading width (<math><msup><mrow><mi>Γ</mi></mrow><mrow><mo>↓</mo></mrow></msup></math>) seems to be independent of temperature and angular momentum. The isospin becomes a good quantum number with increase in temperature. However, when compared with the calculation at high temperature, measured isospin mixing is underpredicted by the calculations.

Exclusive measurement of isospin mixing at high temperature in S

The influence of giant dipole resonance (GDR) induced quadrupole moment on GDR width at low temperatures is investigated experimentally by measuring GDR width systematically in the unexplored temperature range T=0.8–1.5 MeV , for the first time, in A∼100 mass region. The measured GDR widths, using alpha induced fusion reaction, for 97 Tc confirm that the GDR width remains constant at the ground state value up to a critical temperature and increases sharply thereafter with increase in T . The data have been compared with the adiabatic Thermal Shape Fluctuation Model (TSFM), phenomenological Critical Temperature Fluctuation Model (CTFM) and microscopic Phonon Damping Model (PDM). Interestingly, CTFM and PDM give similar results and agree with the data, whereas the TSFM differs significantly even after incorporating the shell effects.

Probing the critical behavior in the evolution of GDR width at very low temperatures in A∼100 mass region