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Predictions of the results of alpha-decay energy (Q-value) and decay half-life ([t.sub.1/2]) are made for experimentally unknown alpha decaying systems of superheavy nuclei. Following a theoretical method proposed recently by B. Sahu, the calculations are performed using the analytical expression of the potential that simulates the nuclear+Coulomb potential of the α + daughter nucleus system. The Q-value considered as resonance energy is calculated using the behavior of the wave function, and the [t.sub.1/2] is expressed analytically using the exact solutions of the potential. A global formula for the potential parameter as a function of neutron number in a given isotopic chain of nuclei is developed for the calculation of Q and [t.sub.1/2]. Calculations of the latter two quantities are made for the decay chain of newly discovered superheavy elements [sup.294]117, [sup.293]117, and for the isotopic chains of Z = 74 and 102. Predictions of the same parameters are made for Z = 113 and some other still unknown superheavy nuclei. It is observed that the global formula works well in evaluating correct results of Q and [t.sub.1/2] for various alpha emitters. PACS Nos: 23.60.+e, 21.10.Tg, 27.70.+q, 27.80.+w, 27.90.+b Nous faisons des predictions sur l'energie de desintegration α (valeur de Q) et la demi-vie ([t.sub.1/2]) pour les desintegrations experimentalement inconnues dans les noyaux super-lourds. Suivant une methode theorique proposee recemment par B. Sahu, les calculs sont faits en utilisant une expression analytique pour le potentiel qui simule le potentiels nucleaire + de Coulomb entre le noyau fille et la particule α. La valeur de Q consideree comme energie de resonance est calculee en utilisant le comportement de la fonction d'onde et [t.sub.1/2] est exprime analytiquement a partir des solutions exactes du potentiel. Afin de calculer Q et [t.sub.1/2], nous developpons une formule globale pour les parametres du potentiel, en fonction du nombre de neutrons dans une chaine isotopique donnee de noyaux. Nous completons le calcul de ces deux quantites pour la chaine de desintegration des elements super-lourds recemment decouverts [sup.294]117, [sup.293]117 et pour les chaines isotopiques Z = 74 et 102. Nous predisons la valeur de ces parametres pour la chaine Z = 113 et pour d' autres super-lourds encore inobserves. Nous notons que la formule globale fonctionne bien et donne des resultats corrects des valeurs de Q et de [t.sub.1/2] pour differents emetteurs α. [Traduit par la Redaction], 1. Introduction Recently, it has been possible to discover many radioactive elements because of progress in theory, experiments, and accelerator-based technologies. Experimentally, alpha-decay of radioactive nuclei is a powerful tool [...]

We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = g, n = 1, 2, ..., N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D( N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D( N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D( N, g). A similar study is presented for case (b). Using the properties of D( N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of g as a function of n and several interesting features of the energy spectrum for different values of g and N are also described. [ABSTRACT FROM AUTHOR]

This paper proves that for N attractive delta function potentials the number of bound states (N) satisfies 1 ≤ N ≤ N in one dimension (1D), and is 0 ≤ N ≤ N in three dimensions (3D). Algebraic equations are obtained to evaluate the bound states generated by N attractive delta potentials. In particular, in the case of N attractive delta function potentials having same separation a between adjacent wells and having the same strength λV, the parameter g= λVa governs the number of bound states. For a given N in the range 1-7, both in 1D and 3D cases the numerical values of g, where n=1,2,..N are obtained. When g=g, N ≤ n where N includes one threshold energy bound state. Furthermore, g are the roots of the Nth order polynomial equations with integer coefficients. Based on our numerical calculations up to N=40, even when N becomes large, 0 ≤ g ≤ 4 and $\frac{{\Sigma g_n }} {N} \simeq 2 $ and this result is expected to be generally valid. Thus, for g > 4 there will be no threshold or zero energy bound state, and if g≈ 2 for a given large N, the number of bound states will be approximately N/2. The empirical formula g = 4/[1+ exp(( N − n)/ β)] gives a good description of the variation of g as a function of n. This formula is useful in estimating the number of bound states for any N and g both in 1D and 3D cases. [ABSTRACT FROM AUTHOR]

We account for the extremely long (∼1018 yr) as well as short (∼10-4 s) lifetimes of &agr; decay in the cases of naturally occurring heavy a emitters with proton number Z = 58-82 and successfully predict the results via an analytical expression for the decay half-life, developed by using an exactly solvable global potential in the theory of potential scattering. [ABSTRACT FROM AUTHOR]

An approach we have proposed recently for calculation of Qα energy and decay half-life Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. on the a decay of radioactive heavy ions is applied to the evaluation of these two important parameters for the nuclei in the superheavy region Z = 112-118 for which experimental data are not available. It is shown that the α + nucleus potential represented by an exactly solvable potential used in the calculation could be expressed in terms of proton (Z) and neutron (N) numbers of the a emitter so that varieties of a-emitting nuclei differing in their Z and N values could be addressed for their decay properties without the help of any adjustable parameter and the results of Qα and Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. for a nucleus are estimated without any prior knowledge of any one of these quantities. This procedure to obtain the values of Qα and Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. works well to reproduce the known experimental results for superheavy nuclei and hence, the procedure is expected to provide proper information about these parameters in experiments on α decay of new nuclei in the superheavy region. [ABSTRACT FROM AUTHOR]

Considering the emission process of α particles in the transition from an isolated quasibound state to a scattering state, a clear expression for the decay width derived in terms of regular Coulomb function, the quasibound state wave function, and the difference of potentials is analyzed. The Schrödinger equation with the effective potential representing the α + nucleus interaction consistent with the potential obtained in the relativistic mean-field approximation is solved exactly for the wave function. Using this exact wave function at resonance and the difference of the above potential from the point charge Coulomb interaction in the expression of decay width stated above, an analytic expression for the decay half-life is derived from the width. By invoking some approximations for different functions in this expression, a closed formula for the logarithm of half-life in terms of characteristic Q value equal to the resonance energy and the mass and charge numbers of the α emitter is obtained. The calculated results of half-life obtained by using the analytic expression of half-life or the closed formula for the logarithm of the half-life are shown to explain the corresponding measured data with values ranging from 10-6 s to 1022 y in the case of large numbers of α emitters that include heavy and superheavy nuclei. The results of the closed formula aligned in a straight line closely explain the rectilinear arrangement of the logarithm values of experimental results for decay half-lives as a function of a quantity that depends on Q values and charge numbers of the emitters. The analytic closed formula with all its terms defined is preferable to the empirical Viola-Seaborg rule of α-decay rate. [ABSTRACT FROM AUTHOR]