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Register a new userAlpha-Cluster formation in heavy alpha-emitters within a multistep model
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$alpha$-decay always has enormous impetuses to the development of physics and chemistry, in particular due to its indispensable role in the research of new elements. Although it has been observed in laboratories for more than a century, it remains a difficult problem to calculate accurately the formation probability $S_alpha$ microscopically. To this end, we establish a new model, i.e., multistep model, and the corresponding formation probability $S_alpha$ values of some typical $alpha$-emitters are calculated without adjustable parameters. The experimental half-lives, in particular their irregular behavior around a shell closure, are remarkably well reproduced by half-life laws combined with these $S_alpha$. In our strategy, the cluster formation is a gradual process in heavy nuclei, different from the situation that cluster pre-exists in light nuclei. The present study may pave the way to a fully understanding of $alpha$-decay from the perspective of nuclear structure.
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The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $alpha$-cluster degrees of freedom are involved and good results are obtained for the excitation of several low-lying states. Within the same model we briefly discuss the expected selection rules for the $alpha$-transfer reactions from $^{12}$C and $^{16}$O.
We study the structure of $^9_Lambda$Be in the framework of three body $alpha+alpha+Lambda$ cluster model using YNG-NF interaction with the Gaussian expansion method. Employing the complex scaling method, we obtain the energies of bound states as well as energies and decay widths of the resonant states. By analyzing our wave functions of bound states and resonant states, we confirm three analogue states of $^9_Lambda$Be pointed out by Band${rm bar{o}}$ and Motoba {it et al.} cite{motoba1983,motoba1985,bando1983}, $^8$Be analogue states, $^9_{Lambda}$Be genuine states and $^9$Be analogue states. The new states of $^9_Lambda$Be are also obtained at a high energy region with broader decay widths.
We present a simple physical model for populating dark matter halos with Lyman Alpha Emiiters(LAEs) and predict the physical properties of LAEs at z~3-7. The central tenet of this model is that the Ly-alpha luminosity is proportional to the star formation rate (SFR) which is directly related to the halo mass accretion rate. The only free parameter in our model is then the star-formation efficiency (SFE). An efficiency of 2.5% provides the best-fit to the Ly-alpha luminosity function (LF) at redshift z=3.1, and we use this SFE to construct Ly-alpha LFs at other redshifts. Our model reproduce the Ly-alpha LFs, stellar ages, SFR ~1-10; Msun/yr, stellar masses ~ 10^7-10^8 Msun and the clustering properties of LAEs at z~3-7. We find the spatial correlation lengths ro ~ 3-6 Mpc/h, in agreement with the observations. Finally, we estimate the field-to-field variation ~ 30% for current volume and flux limited surveys, again consistent with observations. Our results suggest that the star formation, and hence Ly-alpha emission in LAEs is powered by the accretion of new material, and that the physical properties of LAEs do not evolve significantly over a wide range of redshifts. Relating the accreted mass, rather than the total mass of halos, to the Ly-alpha luminosity of LAEs naturally gives rise to the duty cycle of LAEs.
The yrast band in the heavy $N = Z$ nucleus $^{88}$Ru is studied in the framework of the $alpha$-cluster model in combination with double-folding potentials. It is found that the excitation energies of the yrast band in $^{88}$Ru can be nicely described within the $alpha$-cluster approach using a smooth and mildly $L$-dependent adjustment of the potential strength. This result is similar to well-established $alpha$-cluster states in nuclei with a (magic core $otimes$ $alpha$) structure. Contrary, the yrast bands in neighboring $N e Z$ nuclei deviate from such a typical $alpha$-cluster behavior. Finally, the $alpha$-cluster model predicts reduced transition strengths of about 10 Weisskopf units for intraband transitions between low-lying states in the yrast band of $^{88}$Ru.
After recapitulating the procedure to find the bands and the states occurring in the $mathcal{D}_{3h}$ alpha-cluster model of $^{12}$C in which the clusters are placed at the vertexes of an equilateral triangle, we obtain the selection rules for electromagnetic transitions. While the alpha cluster structure leads to the cancellation of E1 transitions, the approximations carried out in deriving the roto-vibrational hamiltonian lead to the disappearance of M1 transitions. Furthermore, although in general the lowest active modes are E2, E3, $cdots$ and M2, M3, $cdots$, the cancellation of M2, M3 and M5 transitions between certain bands also occurs, as a result of the application of group theoretical techniques drawn from molecular physics. These implications can be very relevant for the spectroscopic analysis of $gamma$-ray spectra of $^{12}$C.
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