The running coupling constant is calculated using the imaginary time formalism (ITF) of thermal field theory under the self-energy approximation. In the process, each Feynman diagram in thermal field theory is rewritten as the summation of non-thermal diagrams with coefficients that are functions of mass and temperature. By employing the same mass scale and coupling constant for both the non-thermal QFT and ITF, we derive a relation between them. Also, we calculate the self-energy using ITF, which is equated to the same as that of non-thermal QFT under the zero external momentum limit. This can provide a new expression for the coupling constant. Combining this result with the β(g) and γ_m(g) function relations of the renormalization group equations gives rise to a thermal-dependent coupling constant and running mass. Using these results, the free energy density is evaluated for two-loop order and compared with quasiparticle model.

The experimental evaporation residue cross-sections for the reactions 32S+182W and 32S+184W show large difference in magnitudes, which is unexpected considering that these reactions only differ by two neutrons. To delve into the dynamics of these reactions, thorough coupled-channels calculations and statistical model calculations were conducted. Notably, the experimental capture cross-sections for both reactions were found to be quite similar and were accurately represented by the coupled-channels calculations. However, a significant discrepancy emerged when examining the experimental evaporation residue cross-sections. In the case of the 32S+182W reaction, the evaporation residue cross-sections were reasonably consistent with the predictions of the statistical model calculations. On the contrary, calculations for the 32S+184W reaction not only failed to reproduce the magnitude but also the shape of the observed excitation function. Despite variations in parameters, the statistical model calculations proved inadequate in consistently predicting the evaporation residue cross-sections for the 32S+184W reaction. This suggests a need for further investigation and refinement of theoretical models to better comprehend the intricate dynamics at play in this specific reaction.

Background: Enhanced prescission neutron multiplicity (${\ensuremath{\nu}}_{\mathrm{pre}}$) over statistical model calculations assuming Bohr-Wheeler fission width is explained using Kramers' fission width incorporating dissipative effects. The dissipation strength obtained from such studies reported significant effect of the neutron shell closure of $N=126$ of the fissioning system as well as nuclear temperature. The dependence of dissipation strength on shell effect and temperature is also attributed to the choice of input parameters in the statistical model calculations.Purpose: We investigate the role of $N/Z$, shell effect, collective enhancement of level density (CELD), and excitation energy on ${\ensuremath{\nu}}_{\mathrm{pre}}$ in reactions forming isotopes of the Ra nucleus.Methods: The neutron multiplicity excitation function is measured for the $^{30}\mathrm{Si}+^{182,184,186}\mathrm{W}$ reactions populating $^{212,214,216}\mathrm{Ra}$ nuclei using the National Array of Neutron Detectors (NAND) at the Inter-University Accelerator Centre, New Delhi. Among these compound nuclei, $^{214}\mathrm{Ra}$ has a major neutron shell closure of $N=126$. Measured ${\ensuremath{\nu}}_{\mathrm{pre}}$ are analyzed within the framework of a statistical model incorporating dynamical hindrance in nuclear fission due to dissipation, shell corrections in the fission barrier and level density, and CELD.Results: Experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ show a marginal isotopic dependence at all excitation energies. ${\ensuremath{\nu}}_{\mathrm{pre}}$ values do not show any noticeable effect of neutron magic number $N=126$. Dissipation strength of $\ensuremath{\beta}=8\phantom{\rule{4pt}{0ex}}{\mathrm{zs}}^{\ensuremath{-}1}$ ($5.27\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/\ensuremath{\hbar}$) reasonably reproduces the experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ excitation functions for all three nuclei in the measured energy range. Appreciable variations in presaddle neutron emissions are observed when shell effect or CELD is excluded in the calculations. Even though both the shell and CELD are found to impact primarily in the presaddle sector, they alter the excitation energy and multiplicity in the saddle-to-scission sector as well in a complementary manner.Conclusions: A temperature independent dissipation coefficient is observed to reproduce the experimental results in this study throughout the excitation energy range measured. Shell corrections in fission barrier and level density parameters and CELD in fission and particle evaporation widths also influence the neutron multiplicities. The observed effect of CELD in the presaddle phase is attributed to the large enhancement of level density at the saddle due to its large deformation and consequent enhancement of fission width.

We investigate the influence of neutron emission in the fission of Pa-227 populated by complete fusion of F-19 with Pb-208 at various excitation energies (E*). Mass gated pre-scission neutron multiplicities (.pre) were determined by fragment-neutron angular correlation and time of flight of fission fragments and neutrons using the National Array of Neutron Detectors facility. Obtained Mass - nu(pre) correlation showed that, at lower E* = 24.2 and 32.4 MeV, larger nu(pre) is correlated with asymmetric mass division. On the other hand, at higher E* = 46.1 and 59.6 MeV, larger nu(pr)e is correlated with symmetric mass division. The results were analyzed within the framework of the general description of fission observables GEneral description of Fission observables (GEF) model with multichance fission included. The analysis of fragment mass-total kinetic energy correlation for different chance fission clearly indicates a revival of shell effects at E* = 24.2 and 32.4 MeV as a consequence of sequential fission decay. At these energies, higher chance fission decreases the saddle point excitation energy considerably where shell effects are prominent. The interplay of shell mediated mass asymmetric fission and symmetric fission gives rise to an energy dependent Mass - nu(pre) correlation. We have compared the experimental results with Mass -nu(pre) correlation predicted by the GEF model. It is concluded that the correlation of larger nu(pre) with asymmetric mass at lower excitation energies is a signature of shell effects reinstated by sequential fission decay. At the two higher excitation energies, despite the multichance fission and consequent decrease in saddle point energy, the available excitation energy appears sufficient for the attenuation of shell effects.

Background: Enhanced prescission neutron multiplicity (vpre) over statistical model calculations assuming Bohr-Wheeler fission width is explained using Kramers' fission width incorporating dissipative effects. The dissipation strength obtained from such studies reported significant effect of the neutron shell closure of N = 126 of the fissioning system as well as nuclear temperature. The dependence of dissipation strength on shell effect and temperature is also attributed to the choice of input parameters in the statistical model calculations.Purpose: We investigate the role of N/Z, shell effect, collective enhancement of level density (CELD), and excitation energy on vpre in reactions forming isotopes of the Ra nucleus.Methods: The neutron multiplicity excitation function is measured for the 30Si + 182,184,186W reactions populat-ing 212,214,216Ra nuclei using the National Array of Neutron Detectors (NAND) at the Inter-University Accelerator Centre, New Delhi. Among these compound nuclei, 214Ra has a major neutron shell closure of N = 126. Measured vpre are analyzed within the framework of a statistical model incorporating dynamical hindrance in nuclear fission due to dissipation, shell corrections in the fission barrier and level density, and CELD.Results: Experimental vpre show a marginal isotopic dependence at all excitation energies. vpre values do not show any noticeable effect of neutron magic number N = 126. Dissipation strength of & beta; = 8 zs-1 (5.27 MeV/h over bar ) reasonably reproduces the experimental vpre excitation functions for all three nuclei in the measured energy range. Appreciable variations in presaddle neutron emissions are observed when shell effect or CELD is excluded in the calculations. Even though both the shell and CELD are found to impact primarily in the presaddle sector, they alter the excitation energy and multiplicity in the saddle-to-scission sector as well in a complementary manner.Conclusions: A temperature independent dissipation coefficient is observed to reproduce the experimental results in this study throughout the excitation energy range measured. Shell corrections in fission barrier and level density parameters and CELD in fission and particle evaporation widths also influence the neutron multiplicities. The observed effect of CELD in the presaddle phase is attributed to the large enhancement of level density at the saddle due to its large deformation and consequent enhancement of fission width.

Background: The relevance of including channel coupling effects in the form of target deformation and vibration in fusion reactions has been well established. Many reactions with positive $Q$ values for neutron transfer show enhancement in sub-barrier fusion cross sections. However, there are exceptions to these cases.Purpose: We aim to make a comprehensive list of factors influencing the sub-barrier fusion enhancement in systems with neutron transfer channels having positive $Q$ values.Method: Evaporation residue cross sections were measured for $^{18}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions in the energy range $68--104$ MeV in the laboratory frame, using a recoil mass spectrometer.Results: Inclusion of deformation of target and projectile low-level excitations in the coupled channels calculations explains the measured fusion excitation functions of $^{18}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions.Conclusions: Considering that all the targets have similar deformation, and comparing with $^{16}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions having negative $2n$ transfer $Q$ values, we can conclude that the positive $Q$ values of neutron transfer channels have no effect on the observed fusion cross sections of $^{18}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions.

Using the imaginary time formalism in thermal field theory, we derive the running coupling constant and running mass in two loop order. In the process, we express the imaginary time formalism of Feynman diagrams as the summation of nonthermal quantum field theory (QFT) Feynman diagrams with coefficients that depend on temperature and mass. Renormalization constants for thermal phi 4 theory were derived using simple diagrammatic analysis. Our model links the nonthermal QFT and the imaginary time formalism by assuming both have the same mass scale mu and coupling constant g. When these results are combined with the renormalization group equations and applied simultaneously to thermal and nonthermal proper vertex functions, the coupling constant and running mass with implicit temperature dependence are obtained. We evaluated pressure for scalar particles in two loop orders at the zero external momentum limit by substituting the running mass result in the quasiparticle model.

Background: The relevance of including channel coupling effects in the form of target deformation and vibration in fusion reactions has been well established. Many reactions with positive Q values for neutron transfer show enhancement in sub-barrier fusion cross sections. However, there are exceptions to these cases. Purpose: We aim to make a comprehensive list of factors influencing the sub-barrier fusion enhancement in systems with neutron transfer channels having positive Q values. Method: Evaporation residue cross sections were measured for O-18+W-182,W-184,W-186 reactions in the energy range 68-104 MeV in the laboratory frame, using a recoil mass spectrometer. Results: Inclusion of deformation of target and projectile low-level excitations in the coupled channels calcula- tions - explains the measured fusion excitation functions of O-18+W-182,W-184 ,W-186 reactions. Conclusions: Considering that all the targets have similar deformation, and comparing with O-16+W-182,W-184,W-186 reactions having negative 2n transfer Q values, we can conclude that the positive Q values of neutron transfer - channels have no effect on the observed fusion cross sections of O-18+W-182,W-184,W-186 reactions.

Background: The coupled-channels model has been highly successful in interpreting experimental subbarrier fusion. The statistical model framework has traditionally been used to explain the basic features of composite system de-excitation in the above Coulomb barrier region. However, in $^{12}\mathrm{C}$-induced reactions with $^{182,186}\mathrm{W}$, measured fusion cross sections are significantly lower than those predicted by various theoretical models and by fusion systematics.Purpose: To investigate the dynamics of heavy ion fusion at energies below and above the Coulomb barrier in the $^{12}\mathrm{C}$-induced reactions.Method: A mass spectrometer was used to study the evaporation residues for the $^{12}\mathrm{C}+^{182,184,186}\mathrm{W}$ reactions. The measurements ranged from $12%$ below to $45%$ above the Coulomb barrier energies. The measured fusion cross sections are compared with coupled channels and statistical model calculations.Results: The measured fusion cross sections for $^{12}\mathrm{C}+^{182,184,186}\mathrm{W}$ reactions show reasonably good agreement with coupled-channel calculations. Also, evaporation residue cross sections for $^{12}\mathrm{C}+^{182,184,186}\mathrm{W}$ reactions in the present experiment along with the fission cross sections from literature are described by statistical model calculations.Conclusions: We successfully explain the previously reported discrepancy between fusion measurements and calculations based on various theoretical models and by fusion systematics for $^{12}\mathrm{C}+^{182,186}\mathrm{W}$ reactions.

Background: The coupled-channels model has been highly successful in interpreting experimental subbarrier fusion. The statistical model framework has traditionally been used to explain the basic features of composite system de-excitation in the above Coulomb barrier region. However, in 12C-induced reactions with 182,186W, measured fusion cross sections are significantly lower than those predicted by various theoretical models and by fusion systematics. Purpose: To investigate the dynamics of heavy ion fusion at energies below and above the Coulomb barrier in the 12C-induced reactions. Method: A mass spectrometer was used to study the evaporation residues for the 12C ?+/- 182,184,186W reactions. The measurements ranged from 12% below to 45% above the Coulomb barrier energies. The measured fusion cross sections are compared with coupled channels and statistical model calculations. Results: The measured fusion cross sections for 12C +/- 182,184,186W reactions show reasonably good agreement with coupled-channel calculations. Also, evaporation residue cross sections for 12C & PLUSMN; 182,184,186W reactions in the present experiment along with the fission cross sections from literature are described by statistical model calculations. Conclusions: We successfully explain the previously reported discrepancy between fusion measurements and calculations based on various theoretical models and by fusion systematics for 12C & PLUSMN; 182,186W reactions.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Measurement of the B(E2, 0_1 → 2_1) in the N = 16 nucleus Ne J. Gibelin, D. Beaumel, T. Motobayashi, N. Aoi, H. Baba, Y. Blumenfeld, Zs. Dombradi, Z. Elekes, S. Fortier, N. Frascaria, et al.

Background: Enhancement in fusion cross sections over one-dimensional barrier penetration model (1D-BPM) predictions has been observed at sub-barrier energies owing to the coupling of various internal degrees of freedom to the relative motion. On the other hand, hindrance in fusion is noticed at energies well above the barrier in a few cases. Purpose: The purpose is to probe the dynamics of heavy ion fusion at energies below and well above the Coulomb barrier. Methods: Fusion excitation functions for the O-16 + Nd-142,Nd-150 reactions are measured using the Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Measurements have been performed in the range 12% below to 50% above the Coulomb barrier for both systems. The measured fusion cross sections are compared with coupled channels calculations using CCFULL code. The cross sections are also compared with reactions using O-16 beams with other isotopes of Nd to explore the systematic behavior of fusion. Results: Compared with 1D-BPM predictions, fusion enhancement is observed in both O-16 + Nd-142 and O-16 + Nd-150 reactions at below-barrier energies, with the latter reaction showing a higher enhancement. Coupled channels calculations incorporating the collective excitations of the target nuclei reproduce the fusion cross sections in both reactions. The collective excitations of the projectile nucleus do not seem to contribute to the observed fusion enhancement. Calculations using Akyijz-Winther potential parameters fail to reproduce the fusion cross sections at energies well above the barrier. Conclusions: Fusion enhancement is observed in both reactions studied. Degree of enhancement of sub-barrier fusion cross section is larger for the reaction using Nd-150 target. Fusion hindrance is observed in both reactions at very high energies. The hindrance seems to increase with increasing beam energy. Larger value of diffuseness parameter compared with the value consistent with elastic-scattering measurements is required to reproduce the fusion excitation function at energies well above the barrier. This could be a strong indication of dynamical effects in fusion at very high energies.

The light output response and efficiency of 5 '' x 5 '' BC501A liquid scintillator neutron detectors composing the NAND detector array have been measured by time of flight technique using(252)Cf source. Energy dependent de-tection efficiency was calculated using FLUKA Monte Carlo code and validated by experimental measurement. FLUKA simulation incorporated fission neutron correlation and kinematics of neutron emission from fission source determining the energy distribution of neutrons in the laboratory frame. The intrinsic features of the scintillator were studied by including particle dependent quenching and light output resolution. Comparison of FLUKA simulation of scintillation light produced by neutrons and gamma rays with measurements provided realistic results. The calculated neutron detection efficiency at similar to 0.5 MeV threshold reproduces the experimental data reasonably well in the studied energy range, 0.5 < E-n < 12 MeV. Neutron scattering from target chamber material in NAND was investigated using FLUKA concluding that the loss in neutron flux due to scattering from the chamber wall is similar to 12%. The scattering amounts to background neutron counts in neighbouring detectors comparable to cross-talk events. The absolute efficiency of the NAND array was estimated to be similar to 1.40% after taking into consideration the intrinsic efficiency of liquid cells, geometrical efficiency and flux loss due to scattering.

Background: The onset of a noncompound nuclear fission (NCNF) process such as quasifission was already predicted for heavy symmetric systems with the charge product greater than 1400. However, quasifission is observed indeed in very asymmetric reactions forming Ra-216 with much lower charge product(approximate to 700). A comprehensive idea about the dependence of quasifission on entrance channel mass asymmetry with smaller charge product is still missing. A clear understanding is vital in the production of superheavy elements. Purpose: To investigate limiting value of mass asymmetry near the Businaro-Gallone point where the fusion probability starts to deviate from unity. Method: Evaporation residue (ER) cross sections were measured for O-16,O-18 + Ta-181 reactions at E-lab = 68-110 MeV using a recoil mass spectrometer and compared with coupled-channel and statistical model calculations. Results: Below the Coulomb barrier region, coupled channel calculations reproduced the excitation functions of both O-16,O-18 + Ta-181 reactions. Further, statistical model calculations with the same fission barrier scaling factor k(f) = 0.95 reproduced the experimental ER cross-section energies above the Coulomb barrier. Conclusions: We do not observe any significant signature of fusion suppression in ER excitation functions of O-18 + Ta-181 reaction, in comparison with that of O-16 + Ta-181. This may be attributed to the high resemblance in mass asymmetry and other structural properties of these systems. A fission barrier scaling factor, k(f) = 0.95 used in the statistical model calculations for both systems, explains the experimental ER and fission cross sections, indicating the absence of any NCNF.

The fusion evaporation residue (ER) excitation function has been measured for Cl-35,Cl-37 + Ta-181 reactions at energies above the Coulomb barrier. The measurements were performed using the HYbrid Recoil mass Analyzer at IUAC, New Delhi. Comparable ER cross sections have been observed in both reactions and there is no isotopic dependence. Measured ER cross sections were compared with theoretical calculations employing the dinuclear system model at projectile and target nuclei interaction and statistical model for the deexcitation of the formed compound nucleus. Larger ER cross sections at the complete deexcitation cascade of the formed compound nucleus are noticed in both reactions at higher excitation energies (E* > 80 MeV) over the calculated results. Fusion probability varies from 95% to 40% in the excitation energy range of the study. No appreciable difference in the fusion probability is noticed in the two reactions. Comparison of our results with other reactions populating Th-216 shows a very strong entrance channel dependence.

O+Ta reactions P. Jisha1,∗ A. M. Vinodkumar, B. R. S. Babu, S. Nath, N. Madhavan, J. Gehlot, A. Jhingan, T. Banerjee2,† Ish Mukul2,‡ R. Dubey2,§ N. Saneesh, K. M. Varier, E. Prasad, A. Shamlath, P.V. Laveen, and M. Shareef Department of Physics, University of Calicut, Kerala-673 635, India Inter University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi 110067, India Department of Physics, University college, Thiruvananthapuram-695034, Kerala, India and Department of Physics, School of Physical Sciences, Central University of Kerala, Kasaragod 671316, India

One-neutron pickup reactions for 52 projectile–target combinations were analysed using a systematics between transfer cross-sections and ground-state Q-values. One-neutron pickup transfer shows a good correlation between reduced transfer cross-sections and ground-state Q-values ($$Q_{gg}$$) if one separate the systems into two groups based on their $$Z_{p}Z_{t}$$ product. Also, similar kind of systematics is applied to 2n, 3n and 4n pickup transfer and a good correlation is obtained between reduced transfer cross-sections and $$Q_{gg}$$ values, where no $$Z_{p}Z_{t}$$ dependence is seen.

Neutron multiplicity excitation function has been measured for the Si-30 + Au-197 reaction populating the Np-227 compound nucleus at excitation energies in the range 44.1-78.8 MeV using the National Array of Neutron Detector facility of Inter University Accelerator Centre, New Delhi. Measured pre-scission neutron multiplicity values are analyzed using a statistical model incorporating Krammer's fission width due to the dissipative drag in nuclear fission, shell corrections in fission barrier and level density, collective enhancement of level density, and K-orientation effect. The present work demonstrates that a strong fission hindrance is essential to reproduce the experimental pre-scission neutrons, whereas the temperature dependent dissipation coefficient as observed in a few recent measurements is not required to reproduce the experimental nu(pre) data. No substantial effect of collective enhancement of nuclear level density and tilting away effect of compound nucleus spin on neutron emission prior to the scission configuration was observed unlike fission of preactinides.

J. Gehlot,1,2,* A. M. Vinodkumar,2 N. Madhavan,1 S. Nath,1 A. Jhingan,1 T. Varughese,1 Tathagata Banerjee,1,† A. Shamlath,3 P. V. Laveen,3 M. Shareef,3 P. Jisha,2 P. Sandya Devi,4 G. Naga Jyothi,4 M. M. Hosamani,5 I. Mazumdar,6 V. I. Chepigin,7 M. L. Chelnokov,7 A. V. Yeremin,7 A. K. Sinha,8 and B. R. S. Babu2 1Nuclear Physics Group, Inter University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi 110067, India 2Department of Physics, University of Calicut, Calicut 673635, India 3Department of Physics, School of Mathematical and Physical Sciences, Central University of Kerala, Kasaragod 671314, India 4Department of Nuclear Physics, Andhra University, Visakhapatnam 530003, India 5Department of Studies in Physics, Karnatak University, Dharwad-580003, India 6Tata Institute of Fundamental Research, Mumbai 400005, India 7FLNR, JINR, Dubna 141980, Russia 8UGC-DAE CSR, Indore 452017, India