Empirical relations for the fusion cross sections of heavy ions

Denisov, V. Yu.; Sedykh, I. Yu.

doi:10.1140/epja/i2019-12855-6

Cited by 20 publications

(8 citation statements)

References 103 publications

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“…Rowley and Hagino [17] examined the fusion cross sections of l6 0+ 154 Sm and 12 C+ 12 C with generalized Wong and Hill-Wheeler formulae. Sedykh [18] proposed an empirical relation for the fusion cross-sections of heavy ions.…”

Section: ≤ Z ≤ 112mentioning

confidence: 99%

Empirical model for fusion cross sections of Ca-induced reactions

Rani. L,

Sowmya,

Sridhar

et al. 2024

Chinese Phys. C

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A new empirical formula for the astronomical S-factor has been suggested as a function ofthe Coulomb interaction parameter, center of mass energy, and barrier height. About 22 fusionreactions with 40,48Ca as projectiles were considered for different targets leading to compound nucleiwith the atomic and mass numbers varying between 40 ≤ Z ≤112 and 88 ≤ A ≤278 respectively.The fusion cross-sections have been estimated using the Geometric factor, Gamow-Sommerfieldfactor and empirical formula for the S-factor. A better agreement has been obtained for the presentwork with that of available experiments when compared to Wong’s formula. The present work leadsto a smaller standard deviation value when compared to Wong’s formula when used to correlatewith the experimental data of Calcium-induced fusion reactions. Wong’s formula provides a goodapproximation of fusion cross-sections when center of mass energy is below the fusion barrier whencompared to above the fusion barrier.

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Section: ≤ Z ≤ 112mentioning

confidence: 99%

Empirical model for fusion cross sections of Ca-induced reactions

Rani. L,

Sowmya,

Sridhar

et al. 2024

Chinese Phys. C

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“…To reach this goal, we calculated the theoretical values of the fusion cross section for different colliding systems using the following equation, Herein, the fusion barrier positions and heights can be computed with the help of our analytical parameterized forms On the other hand, one needs to estimate the values of the barrier curvature ÿω 0 for calculating the fusion cross sections. Very recently, Denisov et al [57] attempted to propose an analytical formula for this parameter by analyzing the experimental data of the heavy-ion fusion cross sections over a wide range of masses. Note that the proposed empirical formula, equation (9) of [57], allows us to impose the influence of 1n and 2n transfers between colliding nuclei as well as the coupling to the low-energy surface vibrational states of both nuclei on the energy-dependent behavior of the fusion cross sections.…”

Section: Search For the Quality Of The Present Pocket Formulasmentioning

confidence: 99%

“…Very recently, Denisov et al [57] attempted to propose an analytical formula for this parameter by analyzing the experimental data of the heavy-ion fusion cross sections over a wide range of masses. Note that the proposed empirical formula, equation (9) of [57], allows us to impose the influence of 1n and 2n transfers between colliding nuclei as well as the coupling to the low-energy surface vibrational states of both nuclei on the energy-dependent behavior of the fusion cross sections.…”

Section: Search For the Quality Of The Present Pocket Formulasmentioning

confidence: 99%

“…On the other hand, we only restricted ourselves to formulate the isotopic behavior of the fusion barrier heights and positions. we follow the proposed by Denisov et al [57] to calculate the values of ÿω 0 for different colliding systems. In figures 7 and 8, the parameterized fusion cross sections resulting from equations (17) and (18) for 24 different fusion systems (red solid curves) are compared with their corresponding experimental ones.…”

Section: Search For the Quality Of The Present Pocket Formulasmentioning

confidence: 99%

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Role of nuclear surface tension coefficients in the isotopic dependence of fusion dynamics for neutron-rich colliding nuclei: New parametrization of fusion barriers

Gharaei¹,

Farkhonde²

2020

Phys. Scr.

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A theoretical approach is developed to study systematically the influence of the nuclear surface tension coefficient, γ, of the proximity formalism on the isotopic behavior of the fusion dynamics over a wide range of neutron-rich colliding systems with condition of 1 ≤ N/Z < 1.6 for their compound nuclei. Here six different versions of the surface energy coefficient (γ-PD03, γ-MS67, γ-MS66, γ-MN81-I, γ-MN81-II and γ-MN76) in the calculation of the nuclear potential based on the original proximity potential 1977are employed. It is found that the fusion barrier characteristics and fusion cross sections follow a linear isotopic dependence which is sensitive to the change in the nuclear surface tension between the reacting nuclei. The maximum sensitivity of the data to this technical parameter is obtained for the use of the γ-PD03 version. Further, it is shown that the sensitivity of the isotopic behavior of the fusion cross sections to the coefficient γ increases by decreasing the incident energy. After the calculation of fusion barrier heights and positions using the different versions of proximity potentials, we have searched for their parametrization. Firstly, we present a pocket formula for fusion barriers which is directly dependent on both the coefficient γ and the N/Z ratio of the isotopic systems. Our analysis for the studied isotopic systems reveals that the agreement with the empirical data is improved when we consider the dependence of the analytical parameterized formulas on this coefficient. Further, the fusion cross sections obtained by the present pocket formula are in good agreement with the corresponding experimental data. A comparison with other well known parameterized forms in the context of isotopic studies is also made.

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“…It is clearly visible from these conditions that the total interaction potential V tot (r) plays a key role in the evaluation of heavy-ion fusion reactions. Further, the nucleus-nucleus potential is essential for calculating the fundamental characteristics of this type of nuclear reactions, such as fusion cross sections [1][2][3][4][5]. The properties of the Coulomb component of the potential have already been studied quite well, whereas the situation turns to be more complicated for nuclear part of the nucleus-nucleus potential.…”

Section: Introductionmentioning

confidence: 99%

Systematic study of the isotopic dependence of heavy-ion fusion cross sections at below- and above-barrier energies

Gharaei

Farkhonde

2023

Phys. Scr.

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The present work provides a systematic study on the role of nuclear surface tension in the isotopic dependence of the fusion cross sections at below- and above-barrier energies over wide range of neutron content (0.5 < N/Z < 1.7). To realize our goal, we select three diﬀerent versions of proximity-based potential, involving proximity potential 1977, 1988, and 2010, in order to calculate the nucleus-nucleus potential and ultimately the fusion barrier parameters. It is shown that the barrier positions, heights, and curvatures follow a (second-order) non-linear isotopic behavior with addition of neutrons which are dependent on the eﬀect of variation in the nuclear surface tension. Our ﬁndings reveal that the sensitivity of isotopic dependence of the fusion barrier characteristics to the eﬀect of surface energy coeﬃcients γ increases by increasing the asymmetry of the colliding pair. In addition, we demonstrate the sensitivity toward the coeﬃcient γ is seen more clearly from the more neutron-rich nuclei compared to the neutron-deﬁcient ones. We discuss the isotopic dependence of the fusion cross sections at below- and above-barrier energies within the framework of the Wong model for a single potential barrier. For above-barrier energies, it is shown that the fusion cross sections follow an increasing (second-order) non-linear trend due to the addition of neutrons. While a decreasing (second-order) non-linear trend exists for the variation in the fusion cross sections at below-barrier energies. Simultaneous comparison the results obtained by the 3 versions of proximity potential for the isotopic dependence of fusion cross sections in the mentioned energy regions reveal the importance of the quantum tunneling and also nuclear structure eﬀects.

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Empirical relations for the fusion cross sections of heavy ions

Cited by 20 publications

References 103 publications

Empirical model for fusion cross sections of Ca-induced reactions

Empirical model for fusion cross sections of Ca-induced reactions

Role of nuclear surface tension coefficients in the isotopic dependence of fusion dynamics for neutron-rich colliding nuclei: New parametrization of fusion barriers

Systematic study of the isotopic dependence of heavy-ion fusion cross sections at below- and above-barrier energies

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