Pocket and barrier resonances in potential scattering and their application to heavy-ion reactions

Susan, P.; Sahu, Bidhubhusan; Jyrwa, Betylda; Shastry, C. S.

doi:10.1088/0954-3899/20/8/015

Cited by 10 publications

(7 citation statements)

References 14 publications

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“…The states indicated by (*) are occurring at above-barrier energies and we do not treat them as QB states. They can be designated as above-barrier resonant states [23][24][25]. In table 2 the resonances are listed over a wider range of energy since these are used for further analysis in the next section.…”

Section: Formulationmentioning

confidence: 99%

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

et al. 2009

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In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in onedimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.

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Section: Formulationmentioning

confidence: 99%

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

et al. 2009

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“…The resonances are represented by the poles of S n (k) as stated earlier. In order to obtain the pole position of S-matrix in kplanes we adopted Newton-Raphson iterative method starting with reasonable trial values [20][21][22]. This iterative procedure converges to the pole position, i.e., the zero position of f (−k), fairly fast.…”

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confidence: 99%

“…The later potential has a pocket followed by a more or less flat barrier and was used in an earlier work [22] to make a comparison of pocket and barrier region resonances. It is to be mentioned that the half-width calculated using WKB type barrier penetration formula is independent of the nature of the potential beyond the outer most turning point.…”

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confidence: 99%

Comparison ofS-matrix and WKB methods for half-width calculations

et al. 2006

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The calculated Q values and half widths of α-decay of superheavy elements using both the S-matrix and the WKB methods are analyzed. The calculations are carried out using the microscopically derived α-daughter potentials for the parents appearing in the α-decay chain of super heavy element (A = 277, Z = 112). Both the S-matrix and the WKB methods though yield comparable results for smaller, in fact negative log τ 1/2 values, the former is superior. However, for the case of positive log τ 1/2 it is found that the S-matrix method though exact, runs into some numerical difficulties. With the discovery of many superheavy elements beyond Z = 100 and their decay processes involving, among others, α-decay chains have revived interest in the careful analysis of Q value of α-decay and the corresponding decay constant. The α-decay of super heavy nuclei has been intensively investigated in recent years [1][2][3][4][5][6][7][8][9][10][11]. If α-decay is understood as a two body phenomena involving the daughter and parent nucleus, a proper approach requires a reliable input of α-daughter nucleus potential. These potentials are introduced either phenomenological [e.g., Woods-Saxon (WS) shape with adjustable parameters] or are generated microscopically in the tρρ approximation (double folding model) using explicitly the calculated nuclear (both proton and neutron) densities. Once such a potential is given the usual procedure of calculating Q value and decay constant is to use WKB type approximations to obtain the energies of long-lived states of the effective potential. In the α-decay problem, the effective potential is the sum of the nuclear potential, electrostatic potential and the centrifugal term. This potential generates a huge pocket in between the Coulomb barrier and the centrifugal barrier and in principle can generate bound states with E < 0 and resonant states with E > 0 with finite lifetime. For a typical α-decay system of our interest, the Coulomb barrier height is about 25 MeV, whereas Q values are in the range 5-10 MeV. Because of the long Coulomb tail, at energies near Q value, the barrier width is quite large of the order of 7-8 fm. As a result the resonance which pertains to α-decay will have in most cases, extremely narrow width. Hence resonance energies can be calculated using WKB method applicable for bound states. Thus in such cases, the positive energy resonant states and bound state energies can be expected to satisfy the equationwhere k 2 and V eff (r) are energy and effective potential respectively inh 2 = 2m = 1 units; they have dimension L −2 . The effective potential V eff includes the centrifugal term (l + 1/2 ) 2 /r 2 , as required in the WKB formula. Here r 1 and r 2 denote the two inner turning points.When this formula is used, in general, one gets a number of positive eigenvalues; however, for the study of α-decay, the eigenvalue which corresponds to the Q value of the α-decay is to be identified. Once this eigenvalue is identified, the decay constant can be calculated using the WKB formula in...

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“…[24][25][26] This iterative procedure converges to the pole position, i.e. the zero position of f (−k), fairly fast.…”

Section: Rectangular Barriermentioning

confidence: 99%

Study of Alpha Decay of Super Heavy Elements Using S-Matrix and WKB Methods

Prema

Mahadevan

Shastry

et al. 2008

Int. J. Mod. Phys. E

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A comparative study of the S-matrix and the WKB methods for the calculation of the half widths of alpha decay of super heavy elements is presented. The extent of the reliability of the WKB methods is demonstrated through simple illustrative examples. Detailed calculations have been carried out using the microscopic alpha-daughter potentials generated in the framework of the double-folding model using densities obtained in the relativistic mean field theories. We consider alpha-nucleus systems appearing in the decay chains of super heavy parent elements having A = 277, Z = 112 and A = 269, Z = 110. For negative and small positive log τ 1/2 values the results from both methods are similar even though the S-matrix results should be considered to be more accurate. However, when log τ 1/2 values are large and positive, the width associated with such state is infinitesimally small and hence calculation of such width by the S-matrix pole search method becomes a numerically difficult problem. We find that overall, the WKB method is reliable for the calculation of half lives of alpha decay from heavy nuclei.

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Pocket and barrier resonances in potential scattering and their application to heavy-ion reactions

Cited by 10 publications

References 14 publications

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

Comparison ofS-matrix and WKB methods for half-width calculations

Study of Alpha Decay of Super Heavy Elements Using S-Matrix and WKB Methods

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