Angular momentum effects and barrier modification in sub-barrier fusion reactions using the proximity potential in the Wong formula

Kumar, Raj; Bansal, Manie; Arun, Sham K.; Gupta, Raj K.

doi:10.1103/physrevc.80.034618

Cited by 73 publications

(32 citation statements)

References 22 publications

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“…Interesting enough, the data [1] for the above said 64 Ni+ 100 Mo reaction fit the θ i -integrated (Φ=0 0 ) -summed Wong formula for only the new force GSkI. The other forces (SIII and SV) would apparently need additional barrier modification effects to be added empirically [10]. From the deduced max -values, presented in Fig.…”

Section: Calculationsmentioning

confidence: 83%

“…Eq. (18) gives the barrier height V B , position R B , and the curvaturehω for each , to be used in extended -summed Wong's formula [10], discussed in the following section.…”

Section: The Semiclassical Extended Thomas Fermi (Etf) Modelmentioning

confidence: 99%

“…Carrying out the -summation in Eq. (19) empirically for a best fit to measured cross-section [10], and on integrating over the angles θ i and Φ, we get the fusion cross-section σ(E c.m. ).…”

Section: Extended -Summed Wong Formulamentioning

confidence: 99%

“…Very recently, the Wong formula [9] is also extended by Gupta and collaborators [10,11] to include its angular momentum -summation explicitly, which is also shown to contain the barrier modification effects due to the -dependent barriers. However, for the 58,64 Ni-based fusion-evaporation cross sections [1], a further modification of barriers is found essential for below-barrier energies, which is implemented empirically either by "lowering the barrier" or "narrowing the barrier curvature" by a fixed amount for all 's in the potential calculated by using the proximity potential of Blocki et al [8], with multipole deformations β 2 − β 4 and θ iintegrated for co-planer nuclei.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 discusses the -summed Wong formula [10]. Our calculations are given in section 4, and a brief summary of results in section 5.…”

Section: Introductionmentioning

confidence: 99%

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Barrier modification in sub-barrier fusion reaction⁶⁴Ni+¹⁰⁰Mo using Wong formula with Skyrme forces in semiclassical formalism

Kumar¹,

Gupta²

2011

J. Phys.: Conf. Ser.

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Abstract. We obtain the nuclear proximity potential by using semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), and use it in the extended -summed Wong formula under frozen density approximation. This method has the advantage of allowing the use of different Skyrme forces, giving different barriers. Thus, for a given reaction, we could choose a Skyrme force with proper barrier characteristics, not-requiring extra "barrier lowering" or "barrier narrowing" for a best fit to data. For the 64 Ni+ 100 Mo reaction, the -summed Wong formula, with effects of deformations and orientations of nuclei included, fits the fusion-evaporation cross section data exactly for the force GSkI, requiring additional barrier modifications for forces SIII and SV. However, the same for other similar reactions, like 58,64 Ni+ 58,64 Ni, fit the data best for SIII force. Hence, the barrier modification effects in -summed Wong expression depend on the choice of Skyrme force in semiclassical ETF method. IntroductionThe unexpected behavior of some fusion-evaporation cross sections at energies far below the Coulomb barrier, has challenged the theoretical models to explain the, so called, fusion hindrance phenomenon in true coupled-channels calculations (ccc) for reactions such as 58 Ni+ 58 Ni, 64 Ni+ 64 Ni, and 64 Ni+ 100 Mo [1]. The ccc could, however, be sensitive to the so far unobserved, hence not-included, high-lying states. Misicu and Esbensen [2] were the first who succeeded in describing the above said three reactions in terms of a density-dependent M3Y interaction, modified by adding a repulsive core potential [3]. The repulsive core changes the shape of the inner part of the potential in terms of a thicker barrier (reduced curvaturehω) and shallower pocket. Here, the nuclei are considered spherical in ground-state and the dynamical quadrupole and octupole deformations (β 2 , β 3 ) are included (only β 2 in the case of 58 Ni+ 58 Ni).The dynamical cluster-decay model (DCM) of preformed clusters by Gupta and collaborators [4,5] is found recently [6,7] to have barrier modification effects as the inbuilt property, where "barrier lowering" at sub-barrier energies arise in a natural way in its fitting of the only parameter of model, the neck-length parameter. The difference of actually-calculated barrier from the actually-used barrier height, corresponding to the neck-length parameter for best-fitted fusionevaporation cross section, gives the "barrier lowering" in DCM, whose values are found to increase as the incident energy decreases to sub-barrier energies. Calculations are based on β 2 deformations and orientation θ i -dependent nuclear proximity potential of Blocki et al. [8].

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Section: Calculationsmentioning

confidence: 83%

“…Eq. (18) gives the barrier height V B , position R B , and the curvaturehω for each , to be used in extended -summed Wong's formula [10], discussed in the following section.…”

Section: The Semiclassical Extended Thomas Fermi (Etf) Modelmentioning

confidence: 99%

Section: Extended -Summed Wong Formulamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Section 3 discusses the -summed Wong formula [10]. Our calculations are given in section 4, and a brief summary of results in section 5.…”

Section: Introductionmentioning

confidence: 99%

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Barrier modification in sub-barrier fusion reaction⁶⁴Ni+¹⁰⁰Mo using Wong formula with Skyrme forces in semiclassical formalism

Kumar¹,

Gupta²

2011

J. Phys.: Conf. Ser.

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Fusion dynamics of ¹²C + ¹²C reaction: An astrophysical interest within the relativistic mean‐field approach

2021

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The 12 C + 12 C fusion reaction plays a significant role in the later phases of stellar evolution. For a better understanding of the evolution involved, one must understand the corresponding fusion-fission dynamics and reaction characteristics. In the present analysis, we have studied the fusion cross-section along with the S-factor for this reaction using the well-known M3Y and recently developed R3Y nucleon-nucleon (NN) potential along with the relativistic mean-field densities in double-folding approach. The density distributions and the microscopic R3Y NN potential are calculated using the NL3 * parameter set. Thesummed Wong model is employed to investigate the fusion cross-section, with max-values from the sharp cutoff model. The calculated results are also then compared with the experimental data. It is found that the R3Y interaction gives a reasonable agreement with the data.

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Collective Clusterization in Nuclei and Excited Compound Systems: The Dynamical Cluster-Decay Model

Gupta

2010

Clusters in Nuclei

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Angular momentum effects and barrier modification in sub-barrier fusion reactions using the proximity potential in the Wong formula

Cited by 73 publications

References 22 publications

Barrier modification in sub-barrier fusion reaction⁶⁴Ni+¹⁰⁰Mo using Wong formula with Skyrme forces in semiclassical formalism

Barrier modification in sub-barrier fusion reaction⁶⁴Ni+¹⁰⁰Mo using Wong formula with Skyrme forces in semiclassical formalism

Fusion dynamics of ¹²C + ¹²C reaction: An astrophysical interest within the relativistic mean‐field approach

Collective Clusterization in Nuclei and Excited Compound Systems: The Dynamical Cluster-Decay Model

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Angular momentum effects and barrier modification in sub-barrier fusion reactions using the proximity potential in the Wong formula

Cited by 73 publications

References 22 publications

Barrier modification in sub-barrier fusion reaction64Ni+100Mo using Wong formula with Skyrme forces in semiclassical formalism

Barrier modification in sub-barrier fusion reaction64Ni+100Mo using Wong formula with Skyrme forces in semiclassical formalism

Fusion dynamics of 12C + 12C reaction: An astrophysical interest within the relativistic mean‐field approach

Collective Clusterization in Nuclei and Excited Compound Systems: The Dynamical Cluster-Decay Model

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Barrier modification in sub-barrier fusion reaction⁶⁴Ni+¹⁰⁰Mo using Wong formula with Skyrme forces in semiclassical formalism

Barrier modification in sub-barrier fusion reaction⁶⁴Ni+¹⁰⁰Mo using Wong formula with Skyrme forces in semiclassical formalism

Fusion dynamics of ¹²C + ¹²C reaction: An astrophysical interest within the relativistic mean‐field approach