Systematics of alpha-decay and spontaneous fission half ... · Systematics of alpha-decay and...

Systematics of alpha-decay and spontaneous fission half-lives of super-heavy nuclei

I. SILISTEANU 1, C.I. ANGHEL 1,21 Department of Theoretical Physics, IFIN_HH, Bucharest - Magurele, Romania,

2 University of Bucharest, Faculty of Physics, Bucharest - Magurele, Romania

Purposes

To build systematics of decay properties (data, calculated properties)

To obtain and test new relations for α and SF half-lives

To make use the information on decay properties to derive conclusions concerning the nuclear structure

CONTENTS

1. SIMPLE RELATIONS FOR DECAY HALF-LIVES 1.1 Systematics of α-decay data 1.2 Systematics of Shell Model (SM) α-half-lives (Systematics of calculated -lives with nuclear structure) 1.3 Systematics of “One Body” (ob) α-half-lives (Systematics of calculated -lives without nuclear structure) 1.4 Systematics of Spontaneous Fission half-lives 2. RESULTS 2.1 α-decay half-lives of nuclei with Z=104-118 2.2 α-decay half-lives of nuclei above doubly magic shells, (100)Sn, (208)Pb, (270)Hs 2.3 Extended predictions (298)Fl , (292)120, (304)120. 2.4 Decay properties and valence nucleon numbers

3. CONCLUSIONS and OUTLOOK

Yu.Ts.Oganessian, S.N.Dmitriev, Russ. Chem. Rev., 85 (9) 90-916 (2016)

Chart of Nuclides (2016)

Table 1. Decay properties of superheavy nuclides

Yu.Ts.Oganessian, S.N.Dmitriev, Russ. Chem. Rev., 85 (9) 90-916 (2016)

1. SIMPLE RELATIONS FOR DECAY HALF-LIVES

Fig.1. The simple relation for α-half-lives obtained from the Brown systematics of α-decay data. The parameters of the systematics are given for different (Z-N) parities

B. A. Brown, Phys. Rev. C 46, 811 (1992).

Shell model rate theory (SMRT)

C. I. Anghel and I. Silisteanu, Phys. Rev. C95, 034611 (2017) I. Silisteanu, A. I. Budaca, At. Data Nucl. Data. Tab. 98, (2012) A. I. Budaca, I. Silisteanu, Phys. Rev. C 88, (2013).

Sandulescu, Silisteanu (1976) NPA 272 HO, WS (Wood Saxon) WF

α-SMFA

Mang (1957) Z. Pys. 148, (ideea of D. Jansen, M. G. Mayer-Nuclear Shell Model 1949) HO Wave Funct. (WF)Mang, Rasmussen (1962), Bull. Am. Phys. Soc. Serv. II 8, 315. HO Wave Funct. (Nilsson)

Applications:Sandulescu, Silisteanu, Wunsch (1978) NPA 305 α-decay Ivascu, Silisteanu, (1988) NPA 305 α-decay & Heavy Cluster Emission Silisteanu, Scheid, Sandulescu, (2001) NPA Proton, α-decay & Heavy Cluster Emission

Fig.2. The same as in the Fig.1, but for systematics of calculated shell model (SM) α-half-lives

“One-body” theoryThe asymptotic overlap integral becomes the wave function of relative motion of the fragments at large r values. The corresponding one-body width becomes:

The resonance scattering occurs due to the presence of a quasibound level of the formed nucleus, which is coupled to the scattering state of the decaying system.

G. Breit, Theory of Resonance Reactions and Allied Topics, Enciclopedia of Physics, vol.41/1, 1959, Springer-Verlag,. Berlin.

H. Feshbach, Annals of Physics, vol. 19, 287, (1962).

Single channel case: ? Eigen-function, - values, Depth in origin of nuclear

potential

The same as in the Fig.1, but for systematics of calculated “one-body”(ob) α-half-lives

SPONTANEOUS FISSION

KARPOV, ZAGREBAEV , PALENZUELA, RUI, GREINER Int. J. Mod. Phys. E 21, No. 2 (2012) 1250013

Bf - Muller et al PRC (2015) 91 new even-odd corrections ( extracted from data fit )

The total half-lives of SHN with Z = 104−112 and N = 158−166 calculated from T(fSM) α and T(SF) values as a function of the numbers of valence nucleons (holes) of the doubly magic core (270)Hs. The AD channels starting from parent

nuclei with valence nucleons (marked by arrows) are always terminating at spontaneously fissioning nuclei with nucleon holes.

2.4 Decay properties and valence nucleon numbers

α - Spectroscopic factors

Contributions of the structure effects

Shell corrections of nuclei from the WS4 calculations. The solid and open squares denote the positions of nuclei with (sub)shell closure according to the predicted shell gaps.

N. Wang, et. al., Phys. Rev. C 93, 014302 (2016). 304120

308122

α-half-lives of nuclei above doubly magic shells

186184

N. Wang, et. al., Phys. Rev. C 93, 014302 (2016).

α-decay energies of odd-Z super-heavy nuclei (a) and those of even-Z nuclei (b) from the WS4RBF predictions.

Proton (left panel) and neutron (right panel) canonical s.p. spectra of superheavy nuclide (304)120. The results are extracted from the RHFB calculations with PKOi series and PKA1, and compared to the RHB ones with PKDD and DD-ME2. In all cases the pairing force is derived from the finite range Gogny force D1S with the strength factor f = 0.9.

Schematic illustration of the alpha decay. For an even-even nucleus the least bound pairs of nucleons are combined to form the alpha particle. In an odd–even nucleus the first pairs are usually used to form the alpha (bottom) leaving the daughter nucleus in an excited state, rather than breaking one pair.

Table 1. The experimental and calculated (*) α-half-lives for spherical (Te, Po and 122) and deformed (Ds, Lv and 126) nuclei with (sub) shell closure according to the predicted shell gaps.

Z=120, N=172, 184 have α-decay properties similar

to (100)Sn and (208)Pb (spherical nuclei).

Oganessian et al., Phys. Rev. C 79, 024603 (2009).

“Attempt to produce element 120 in the (244)Pu+(58)Fe reaction”

-the element Z=120 has not been confirmed.

The main decay channel is Spontaneous Fission.

3.1 T^(fSM) well reproduce T^(fexp) and T^(exp).

Spectroscopic factors experimental and theoretical have close values.

3. CONCLUSIONS and OUTLOOK

The simple relation for α-half-lives obtained from the Brown systematics of α-decay data. The parameters of the systematics are given for different (Z-N) parities

The simple relation for α-half-lives, but for systematics of Calculated shell model (SM) α-half-lives.

Experimental and calculated α decay and spontaneous fission and total half-lives for isotopes of Hs.

Experimental and calculated α decay and spontaneous fission and total half-lives for isotones N=162.

3.2 Half-lives and reaction energies for α-decay and spontaneous fission exhibit pronounced odd-even (Z-N)

staggering effects and strong particle-number dependence attributed to nucleonic paring.

α

α

α

α0 α1 α2

Magic Nuclei

Tα (104 Te)= Tα (212 Po)= Tα (Z=120) Tα (302 Lv) = ?

GROUPSimilar chemical Properties for the constant number of valence electrons

PERIOD

Similar (~ equal) α-decay half-lives for the constant number of valence nucleons (alphas)

3.3 Decay properties are controlled by the number of valence nucleons (α particles)

The experimental α-half-lives of trans-tin (open symbols) and trans-lead (full symbols) nuclei versus Casten-Zamfir factor P=Np*Nn/(Np+Nn). The calculated half-lives for Cs and Ba isotopes are connected by dot lines.

I. Silisteanu, W. Scheid and A. Sandulescu, Nucl. Phys. A 679, 317-336 (2001).

P factor represents the number of α particles (holes) over (below) the magic shell.

3.4 At the closed shells of nucleons, nuclear binding energies and lifetimes increase strongly, while reaction energies markedly decrease, these give rise to the most stable nuclear shapes in the ground state.

3.5 The studies of nuclear decay properties are providing:

* a deep insight into the accuracy of modern approaches for the structure of SHN, * stringent new tests of our theoretical understanding.

Thank You For Your Attention!