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![Comparison of theoretical fusion barrier heights V theor B (MeV) using different proximity potentials with experimental values V expt B (MeV) [19–25]. The solid lines represent the straightline least-squares fit created over different points.](profile/Ishwar-Dutt/publication/256504357/figure/fig1/AS:392723824693248@1470644064298/Comparison-of-theoretical-fusion-barrier-heights-V-theor-B-MeV-using-different.png)
Comparison of theoretical fusion barrier heights V theor B (MeV) using different proximity potentials with experimental values V expt B (MeV) [19–25]. The solid lines represent the straightline least-squares fit created over different points.
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By using 14 different versions and parametrizations of a proximity potential and two new versions of the potential proposed in this paper, we perform a comparative study of fusion barriers by studying 26 symmetric reactions. The mass asymmetry η A = (A 2 −A 1 A 2 +A 1), however, is very large. Our detailed investigation reveals that most of the pro...
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... Fig. 3 are taken directly from the literature [19][20][21][22][23][24][25]. The limited numbers of reactions in certain cases are caused by the restrictions posed on different potentials [3,9,[14][15][16]. The lines are the fits over the points. These fitted equations distinguish the deviation from the experimental data. Very interestingly, ...
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![Figure 3: Same as Figure 2, but for ∆V B (%) [Define in Eq. (9)].](profile/Ishwar-Dutt/publication/261296511/figure/fig2/AS:667834740908032@1536235618075/Same-as-Figure-2-but-for-V-B-Define-in-Eq-9_Q320.jpg)
By using different isospin dependent proximity-type potentials, we performed a
detailed study of neutron/proton-rich colliding nuclei with N/Z ratio between 0.5 and 2.0.
Isotopes of three different series namely, Ne-Ne, Ca-Ca, and Zr-Zr are taken into account. A
monotonous increase (decrease) in the fusion barrier positions (heights) using a uni...
Citations
... The nature of Coulomb and centrifugal parts of the ion-ion potential is well known while many ambiguities are associated with the nuclear part. Consequently, several approaches have been proposed to describe the nuclear part of the interaction potential [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. These approaches, however lead to different values of barrier parameters for the same reactants, particularly when one of reactant is light. ...
Fusion cross section for reactions induced by weakly bound nuclei ⁶He, 6,7Li 9,11Be and ¹⁰B on targets lying in the mass region 64 ≤ A ≤ 238 have been investigated at around Coulomb barrier energies within the coupled channel formalism. Specifically, the effects of coupling to low-lying excited states of reactants and those arises due to the breakup of projectile have been studied by using Broglia and Winther (BW91), Aage Winther (AW95) and fitted potential (FP) parameterization schemes. Among these the FP scheme is found to be most appropriate in the description of fusion excitation functions of various projectile-target combination. Further, it is observed that in the sub barrier energy region there is an enhancement in the fusion cross section due to coupling to excited states while there occurs fusion suppression at above barrier energies because of the breakup of the projectile.
... Since introducing the phenomenological proximity potential by Blocki et al [10] in 1977, researchers have developed, modified, and generalized this potential to explain the fusion process of nuclei as well as the alpha and other cluster decay of nuclei [11][12][13][14][15][16][17][18][19][20][21]. This practical potential is made of two parts; one depends on the geometry of colliding nuclei (nuclei radius, surface energy [22,23], and surface width or thickness); the other one is a universal function that depends on the surface distance of colliding nuclei. ...
Accurate evaluation of alpha decay half-life is important for understanding nuclear stability, ensuring nuclear safety, optimizing medical treatments, and studying astrophysical processes. Considering the deformed shape of nuclei, we calculated the alpha-decay half-life of 359 nuclei using the proximity potential. In addition, we employed the Wentzel-Kramers-Brillouin approximation to compute the penetration probability through the potential barrier comprising nuclear, Coulomb, and centrifugal potentials. Our calculations revealed that the penetration probability, and hence the alpha-decay half-life, depend on the direction of alpha particle emission relative to the axial symmetry of the parent nuclei. Furthermore, our results suggested that the dependence of alpha-decay on parent nuclei temperature needs to be reassessed. We tabulated the alpha-decay half-life for various nuclei, and our results shown better agreement with experimental data compared to theoretical data in the literature.
... It includes a geometric factor and a universal function. Various proximity potentials which can change with the parameters such as the radius parameter, surface energy coefficient and universal function can be obtained from the literature [32][33][34][35][36]. As a result of these, we are looking for alternative nuclear potential(s) for the analysis of the 26 Mg( 3 H, 2 H) 27 Mg transfer reaction. ...
The angular distribution of the 26Mg(3H,2H)27Mg reaction at 36 MeV incident energy is reanalyzed by using the distorted wave Born approximation (DWBA) method. Four forms of the optical model potentials such as temperature dependent and temperature independent density distributions, different nuclear potentials, and different nucleon-nucleon interactionsare used to determine the effect on the 26Mg(3H,2H)27Mg transfer reaction of the entrance channel. These analyses display the similarities and differences of all the approaches which are discussed in this work, and provide alternative density, alternative nuclear potential and alternative nucleon-nucleon interactions.
... With the passage of time, different theoretical models have been proposed to evaluate the strength of the potential energy of nuclear interaction during the fusion process [6][7][8][9][10][11][12]. The proximity potential formalism [13] is one of the most important and widely used approaches to obtain the nuclear part V N (r), see for example [3,[14][15][16][17]. As a result of the literature, this formalsim enables us to analyze the influence of various physical effects such as surface energy coefficients and nuclear surface diffuseness in the fusion of heavy-ions [18][19][20]. ...
... 2010 in Refs. [16][17][18]21]. ...
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.
... We note that the nuclear proximity potential can be described as the product of two factors: one is a geometrical factor depending upon the mean curvature of the interacting surfaces, and the other is a universal function depending upon the separation distance. The various versions of nuclear proximity potentials are available in the literature [32][33][34][35][36][37][38][39][40]. In recent years, many researchers have performed comparative studies of different versions of proximity potentials for describing alpha and cluster radioactivity half-lives [41][42][43]. ...
... 81 (set I, II and III) [55], Prox. 88 [33], Prox. 2010 [34], Prox. ...
... It should be mentioned that different versions of the proximity potential have been used for studying the alpha and cluster decay processes; see for example Refs. [32][33][34][35][36][37][57][58][59]. Here and in the following we present the theoretical details of the different proximity potentials that we used in this study. ...
Within the framework of 16 different versions of proximity potentials, we study the alpha decay half-lives of 21 probable isotopes of nuclei around \(N=Z\) in the range of \(52\le Z\le 56\). The obtained results show that the theoretical half-lives of the Prox. 81 (set III) and Prox. 88 potential models are in very close agreement with the available experimental data. For comparison, the validity of the generalized liquid drop model (GLDM) and effective liquid drop model (ELDM) are also evaluated in reproducing the experimental data of alpha radioactivity half-lives. On the basis of the isotopic dependence of the Coulomb potential barrier and the released energy \(Q_{\alpha }\), we discuss the variation in the penetration probability of \(\alpha \)-particle and alpha decay half-lives with neutron content. The validity of the Geiger–Nuttall (GN) law is examined for \(\alpha \) transitions from the ground state of the selected parent nuclei. The values produced by the present proximity potentials are compared with those obtained by some of the well-known empirical and semi-empirical formulae, including Royer, SemFIS (semi-empirical relationship based on fission theory), Akrawy, MRenB, YQZR, MYQZR, and AKRA. The computed standard deviations of the calculated half-lives in comparison with the experimental data suggest that the SemFIS formula produces the lowest standard deviation among the different formulae for alpha decay of the present nuclei. The present approaches are also employed to predict the alpha radioactivity half-lives for parent nuclei at around \(N=Z\) whose the experimental data are not available for them.
... It provides a simple formula for the nucleus-nucleus interaction energy described as the product of a factor determined by the mean curvature of the interaction surface and an universal function (depending on the separation distance), which is independent of the masses of colliding nuclei. Recently, several authors performed a comparative studies of various proximity potential formalism for reseraching fusion, quasi-elastic scattering and fusion, α decay, proton radioactivity, cluster decay and heavy particle radioactivity [49][50][51][52][53][54][55][56]. Among these proximity potential formalism, they obtained the optimal version of proximity potential formalism to describe the corresponding processes. ...
... In this work, we extend the CPPM to study the half-lives of 2p radioactivity with 26 different versions of proximity potential formalisms, which are : (i) Prox.77 [48] and its 12 modified forms on the basis of adjusting the surface energy coefficient γ 0 and k s [71][72][73][74][75][76][77][78][79], (ii) Prox.81 [80], (iii) Prox.00 [81] and its revised versions Prox.00DP [55], Prox.2010 [82] and Dutt2011 [83], (iv) Bass73 [84,85] and its revised version Bass80 [86], (v) CW76 [87] and its revised version AW95 [88], (vi) Ng o80 [89], (vii) Denisov [90] and its revised version Denisov DP [55], (viii) Guo2013 [91]. The more detailed expressions for these proximity potential formalisms are listed in the following. ...
... In this work, we extend the CPPM to study the half-lives of 2p radioactivity with 26 different versions of proximity potential formalisms, which are : (i) Prox.77 [48] and its 12 modified forms on the basis of adjusting the surface energy coefficient γ 0 and k s [71][72][73][74][75][76][77][78][79], (ii) Prox.81 [80], (iii) Prox.00 [81] and its revised versions Prox.00DP [55], Prox.2010 [82] and Dutt2011 [83], (iv) Bass73 [84,85] and its revised version Bass80 [86], (v) CW76 [87] and its revised version AW95 [88], (vi) Ng o80 [89], (vii) Denisov [90] and its revised version Denisov DP [55], (viii) Guo2013 [91]. The more detailed expressions for these proximity potential formalisms are listed in the following. ...
In this work, we study the two-proton ($2p$) radioactivity half-lives for nuclei near or beyond the proton drip line within the Coulomb and proximity potential model (CPPM). We investigate the 28 versions of proximity potential formalisms, which were proposed for heavy-ion fusion reactions, heavy-ion elastic scattering, ternary fission and other applications. The results indicate that BW91 and Bass77 are inappropriate for handling $2p$ radioactivity since the classical turning point $r_{in}$ cannot be obtained for the depth of the total interaction potential between the released two protons and daughter nucleus being greater than the $2p$ radioactivity released energy. Among the other 26 proximity potential formalisms, the one proposed by Royer \textit{et al.} in 1984 denoted as Prox.77-8 is the best version with the lowest rms deviations between experimental data and relevant theoretical results. It is worth mentioning that the calculations of Coulomb and Proximity Potential Model for Deformed Nuclei [PRC 104, 064613 (2021)] has least standard deviation ($\sigma$=0.592) compared with present model and other models/formulae. Furthermore, we use CPPM with Prox.77-8 to predict the $2p$ radioactivity half-lives of 35 potential candidates whose $2p$ radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are consistent with previous theoretical models such as the unified fission model (UFM), generalized liquid drop model (GLDM) and effective liquid drop model (ELDM).
... One is characterised by the fusion reaction when the two nuclei fuse to form a compound nucleus and the other by the QEL scattering when the two nuclei enter barely into the strong force regime [2,3] keeping their identities almost intact. However, many a time the distinction is overlooked, see, for example [13,14], though the concept was introduced in the seventies [2,3]. It is worth noting here that it is only Bass who has segregated the appearance of the Coulomb barrier in the two different ways mentioned above: one is the Bass interaction model and the other is the Bass fusion model [2,3]. ...
We have constructed empirical formulae for the fusion and interaction barriers using a large number of experimental values chosen randomly from the literature available till date. The obtained fusion barriers have been compared with different model predictions based on the proximity, Woods–Saxon and double folding potentials along with several empirical formulas, time-dependent Hartree–Fock theories and experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for the reactions meant for the synthesis of superheavy elements also. Furthermore, it is seen that substitution of the predicted fusion barrier and radius in classic Wong formula (Wong, Phys. Rev. Lett.31:766 (1973) for the total fusion cross-sections agrees very well with the experiments. Similarly, current interaction barrier predictions have also been compared well with a few experimental results available and Bass potential model meant for the interaction barrier predictions. Importantly, the present formulae for the fusion as well as interaction barrier will have practical implications in carrying out physics research near the Coulomb barrier energies. Furthermore, the present fusion barrier and radius provide us with a good nucleus–nucleus potential which is useful for numerous theoretical applications.
... It is said in Ref. [7] that the experimental fusion barriers are always lower than the theoretical bare potentials, which is the result of coupling to high energy collective states. Other studies indicate similar results and show a preference for certain theoretical potential [14,22,40,41]. To see the difference between the result of V MCW B and other bare potentials, we compare this result with the results of 15 potential models in Fig. 3. ...
The synthesis of superheavy elements based on fusion reactions and multinucleon transfer reactions is sensitive to the reaction energies, where the Coulomb barrier plays a crucial role as it must be overcome for the projectile and target to contact each other. The Coulomb barrier cannot be measured directly, and the synthesis of superheavy elements is sensitive to it. In this study, we systematically extract the barrier information from the experimental fusion excitation functions by the empirical cross section formula, which is based on a single-Gaussian distribution of fusion barrier heights. A total of 403 sets of experimental data are fitted, among which 243 sets have good results with χ2/pt less than one. The extracted fusion barrier is a dynamical barrier, which includes the overall effect of coupled channels. Different from the prediction of the WKJ formula, the new scaling law proposed in this work is almost identical to the CW76 Coulomb barrier at the z=170–300 region and reproduces well the centroid barrier extracted from quasielastic scattering. The comparison to the other 14 bare potential models and exploration of the very large z region is also discussed. It is also remarkable to find that the predictions of the DP2015 potential, including of the contributions of the macroscopic and shell correction terms, are highly consistent with the extracted results in this work and the CW76 potential. The numerical results demonstrated that the dynamical fusion barrier and the centroid barrier extracted from the quasielastic reaction (the reaction threshold) could be the same physical quantity for superheavy reactions. This study could provide important references for the synthesis of superheavy nuclei based on fusion reactions and very heavy multinucleon transfer reactions.
... Within these approaches and empirical formulas, the experimental radioactivity halflives are reproduced with different accuracies. The proximity potential based on the proximity force theorem was firstly put forward by Blocki et al. [56] and widely applied to nuclear physics [57][58][59][60][61][62][63][64][65][66], such as heavyion fusion reaction [67], heavy-ion elastic scattering [68], fusion barriers [69], etc. For its simple and accurate formalism with the advantage of adjustable parameters, using the proximity potential to replace the nuclear potential, Santhosh et al. proposed the Coulomb and proximity potential model (CPPM) [70] to deal with cluster radioactivity in 2002. ...
In the present work, considering the preformation probability of the emitted two protons in the parent nucleus, we extend the Coulomb and proximity potential model (CPPM) to systematically study two-proton (2p) radioactivity half-lives of the nuclei close to proton drip line, while the proximity potential is chosen as Prox.81 proposed by Blocki et al. in 1981. Furthermore, we apply this model to predict the half-lives of possible 2p radioactive candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2016. The predicted results are in good agreement with those from other theoretical models and empirical formulas, namely the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), Gamow-like model, Sreeja formula and Liu formula.
... The nuclear potential of the original proximity potential 1977 (Prox. 77) [35] is given by ...
... Here, is the distance between the near surfaces of two reacting nuclei, is the mean curvature radius, and is the universal function [35][36][37]. In addition, represents the width of the nuclear surface and is considered to be 1 fm. ...
A systematic survey of the accurate measurements of heavy-ion fusion cross sections at extreme sub-barrier energies is performed using the coupled-channels (CC) theory that is based on the proximity formalism. This work theoretically explores the role of the surface energy coefficient and energy-dependent nucleus-nucleus proximity potential in the mechanism of the fusion hindrance of 14 typical colliding systems with negative -values, including ¹¹ B+ ¹⁹⁷ Au, ¹² C+ ¹⁹⁸ Pt, ¹⁶ O+ ²⁰⁸ Pb, ²⁸ Si+ ⁹⁴ Mo, ⁴⁸ Ca+ ⁹⁶ Zr, ²⁸ Si+ ⁶⁴ Ni, ⁵⁸ Ni+ ⁵⁸ Ni, ⁶⁰ Ni+ ⁸⁹ Y, ¹² C+ ²⁰⁴ Pb, ³⁶ S+ ⁶⁴ Ni, ³⁶ S+ ⁹⁰ Zr, ⁴⁰ Ca+ ⁹⁰ Zr, ⁴⁰ Ca+ ⁴⁰ Ca, and ⁴⁸ Ca+ ⁴⁸ Ca, as well as five typical colliding systems with positive -values, including ¹² C+ ³⁰ Si, ²⁴ Mg+ ³⁰ Si, ²⁸ Si+ ³⁰ Si, ³⁶ S+ ⁴⁸ Ca, and ⁴⁰ Ca+ ⁴⁸ Ca. It is shown that the outcomes based on the proximity potential along with the above-mentioned physical effects achieve reasonable agreement with the experimentally observed data of the fusion cross sections , astrophysical factors, and logarithmic derivatives in the energy region far below the Coulomb barrier. A discussion is also presented on the performance of the present theoretical approach in reproducing the experimental fusion barrier distributions for different colliding systems.
