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Publicly Available Published by De Gruyter April 2, 2019

Prediction of Alpha Decay Half-Lives of Z = 118–121 Superheavy Nuclei with A ≤ 300 by Using the Double-Folding Potential

  • M. Sayahi , V. Dehghani , D. Naderi and S.A. Alavi EMAIL logo

Abstract

The alpha decay half-lives of Z = 118–121 superheavy nuclei with A ≤ 300 are calculated by using the density-dependent nuclear potential in the framework of the WKB method. The Paris and Ried M3Y nucleon-nucleon potentials are used in the calculation of the double-folding potential, which the Paris potential predicts to be the larger value of the half-lives. The obtained half-lives with Paris parameterisation are compared with those using three semi-empirical formulas, namely the improved Sahu formula, the universal decay law for alpha decay, and the formula for both alpha decay and cluster decay. The predicted half-lives with double-folding lie in between the improved Sahu and universal decay law formulas for both alpha and cluster decay. However, it is closer to the universal decay law formula and obeys its trend in all the studied superheavy nuclei.

1 Introduction

The study of superheavy nuclei is one of the hot topics of recent nuclear physics research, both theoretically and experimentally [1], [2], [3], [4], [5], [6], [7], [8], [9]. Currently, 294Og is the heaviest synthesised nucleus, and lighter and heavier isotopes of Z = 118 and Z > 118 are unknown. Therefore, the study of the structure, decay modes, and decay half-lives of superheavy nuclei is of great importance for future studies. Alpha decay is one of the dominant decay modes of superheavy nuclei, and the determination (measurement or calculation) of the alpha decay half-life is crucial for the synthesis and study of superheavy nuclei.

Several theoretical studies have predicted the alpha decay half-lives of superheavy nuclei [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. In these studies, different models and nucleus-nucleus potentials have been used for the determination of the alpha decay half-lives. For instance, in [6] the alpha decay half-lives of some superheavy nuclei with Z = 106–134 have been predicted using a modified generalised liquid drop model (GLDM). In [10], the predicted half-lives are given by using the double-folding potential for some even-even superheavy nuclei with Z = 104–120. In [15], the alpha decay half-life of Z = 119–120 superheavy nuclei is calculated within the Coulomb and proximity potential model for deformed nuclei. In [20] and [21], by using GLDM, the calculated half-lives of Z = 62–118 even-even nuclei and predictions of the decay chain of the superheavy nuclei 293,295–297Og are given.

Different decay modes of superheavy nuclei Z = 122, Z = 124, and Z = 126 were investigated in [22], [23], [24], [25], [26]. A semi-empirical formula for the alpha decay half-lives of superheavy nuclei with Z < 136 is given in [27]. Actinides are alpha emitters with noticeable deformation. In [28], a pocket formula for the deformation parameters of these nuclei is represented.

In our recent work [29], the role of a constant value of the surface parameter in the alpha decay half-life calculations of 68 known superheavy nuclei was investigated using the phenomenological deformed Woods–Saxon nuclear potential. Because of the importance of a systematic study on the alpha decay half-lives of superheavy nuclei, we were motivated to calculate the half-lives of 66 unknown (Z = 118–121) superheavy nuclei with A ≤ 300 by using a double-folding potential with two (Paris and Ried M3Y) nucleon-nucleon potentials. In this study, our aims were as follows: (i) to test the employed theoretical model for the calculation of the half-lives of 23 isotopes of Fr and 19 isotopes of Ra nuclei; (ii) to determine the half-lives of 66 unknown superheavy nuclei and 294Og; (iii) to compare the calculated half-lives with the Ried and Paris potentials; (iv) to comare the calculated half-lives with those using three semi-empirical formulas; and (v) to analyse the role of alpha pre-formation probability in the theoretical calculation of the half-lives.

In Section 2, the method of calculation is introduced, and in Section 3 the obtained results are given. Finally, concluding remarks are given in Section 4.

2 Theoretical Method

By using semi-classical WKB (Wentzel–Kramers–Brillouin) approximation, the alpha decay half-life (T1/2) is calculated as

(1)T1/2=ln2νPS,

where ν, P, and S are the assault frequency, tunnelling probability, and alpha pre-formation probability, respectively. The average value of the assault frequency is obtained as [30]

(2)ν=0π/2dθsin(θ)ν(θ),

where the assault frequency ν(θ) at each angle is given as

(3)ν(θ)=2μ[r1(θ)r2(θ)dr2μ2|QαV(r,θ)|]1.

The probability of tunnelling of the alpha particle through the barrier with sub-barrier energies is given as

(4)P=0π/2dθsinθ1+eq(θ),
(5)q(θ)=22μr2(θ)r3(θ)drV(r,θ)Qα,

where Qα is the energy released in the alpha decay process, and V(r,θ) is the effective potential between the axially symmetric deformed daughter nucleus and the alpha particle. ri(θ) are the turning points, and μ is the reduced mass of the alpha-daughter system.

The effective potential includes the attractive nuclear potential VN, the repulsive Coulomb potential VC, and the additional repulsive centrifugal part Vcf, and is given by

(6)V(r,θ)=λ(θ)VN(r,θ)+VC(r,θ)+Vcf(r),

where λ is a normalisation factor. Based on double-folding method, the nuclear potential VN or Coulomb potential VC can be calculated as [31]

(7)VN(C)(r,θ)=dr1dr2ρα(r1)v(s)ρd(r2),

where s=|r2r1+r| is the relative distance between the interacting nucleon pair, v is the nucleon-nucleon interaction potential, and ρα(r1) and ρd(r2) are the matter density distributions of the cluster and daughter nucleus, respectively. The matter density distribution of the alpha cluster in Gaussian form is given as [31]

(8)ρα(r1)=0.4229e0.7024r12.

The matter (charge) density distribution of the daughter nucleus can be calculated as

(9)ρd(r2,θ)=ρ01+exp[r2R(θ)a(θ)].

The orientation-angle-dependent half-density radius is given by

(10)R(θ)=R0(1+β2Y20(θ)+β4Y40(θ)),

with the parameter R0=1.07Ad1/3fm [32]. β2 and β4 are the quadrupole and hexadecapole deformation parameters of the daughter nucleus. The deformed surface diffuseness is written as [33]

(11)a(θ)=a(θ)1+|R(θ)|r=R(θ)|2,

where the proposed a(θ)=a0(1+β2Y20(θ)), with a0=0.54fm [32].

In (7), the Paris and Ried M3Y effective nucleon-nucleon interaction is given by [34]

(12)vParis(s)=11062e4s4s2537e2.5s2.5s+J00Parisδ(s),
(13)vRied(s)=7999e4s4s2134e2.5s2.5s+J00Riedδ(s).

The first and second terms are responsible for the direct part, and last term is responsible for the exchange part of the double-folding potential. The Ried and Paris zero-range pseudo-term is written as [34]

(14)J00Paris=592(10.003Elab/Aα),
(15)J00Ried=276(10.002Elab/Aα),

where Elab=Qα(Ad/Ap).

It is worth noting that the density-dependent M3Y (DDM3Y) effective interaction is more accurate and standard than M3Y [13]. Nevertheless, because of the comparative goal of this work, the M3Y potential is employed in the calculations.

The Coulomb potential is calculated by using the proton-proton potential

(16)v(s)=e24πε01s.

The integral of (7) can be evaluated numerically by using the multi-pole expansion method of density distribution and Fourier transformation of the density distribution and local two-body effective interaction [32], [34], [35].

In order to guarantee the first turning point, the centrifugal potential with Langer modification is written as [30]

(17)Vcf(r)=2(l+1/2)22μr2,

where μ is the reduced mass of the alpha-daughter system, and l is the orbital angular momentum of the alpha particle.

The normalisation factor λ(θ) is determined using the Bohr–Sommerfeld quantisation condition for alpha decay [32], [36]

(18)r1(θ)r2(θ)dr2μ2[QαV(r,θ)]=(Gl+1)π2,

where the parameter G is the global quantum number [32]:

G=(22N>126,2082<N126,18N82.

One of the alpha particle pre-formation probability formulae is written as [37]

(19)logS=p1+p2(ZpZ1)+p3(NpN1)+p4Ap,

where the updated data of Pi are presented in Table 1 of [39]. An alternative empirical formula for the pre-formation probability that has been proposed for heavy and superheavy nuclei is given by [40]

Table 1:

Alpha decay half-lives of Fr and Ra isotopes.

Alpha decay(β2,β4)Qα(exp)(MeV)lminlogT1/2(R)logT1/2(P)logT1/2(emp)1logT1/2(emp)2logT1/2(exp)
200Fr → 196At(−0.217, 0.017)7.620−1.597−1.318−1.252−1.541−1.31
201Fr → 197At(−0.207, 0.015)7.520−1.258−0.973−0.911−1.222−1.161
202Fr → 198At(−0.207, 0.015)7.3890−0.825−0.537−0.56−0.823−0.429
203Fr → 199At(0.096, 0.003)7.260−0.401−0.121−0.096−0.407−0.238
204Fr → 200At(0.096, 0.003)7.170−0.1030.1930.216−0.1170.434
205Fr → 201At(0.086, −0.009)7.05500.3160.6050.6280.2730.593
206Fr → 202At(0.086, −0.009)6.9200.8151.0931.2360.7331.280
207Fr → 203At(−0.083, 0.014)6.900.9041.1861.2410.8011.193
208Fr → 204At(−0.084, 0.002)6.7701.3991.6852.0231.2611.822
209Fr → 205At(−.073, 0.002)6.7801.3631.6411.7951.2271.754
210Fr → 206At(−0.073, 0.002)6.6722.0632.3432.9711.6122.429
211Fr → 207At(−0.053, −0.011)6.6601.7762.0732.3711.6312.330
212Fr → 208At(−0.042, −0.023)6.5322.6042.8963.9492.1424.106
213Fr → 209At(0.011, 0)6.9100.7521.0311.1480.6891.542
214Fr → 210At(0.011, 0)8.595−3.469−3.1902−2.872−4.558−2.270
215Fr → 211At(0, 0)9.540−7.191−6.929−6.619−6.895−7.066
216Fr → 212At(0.011, 0.012)9.170−6.580−6.2905−5.390−6.060−6.133
217Fr → 213At(−0.011, 0)8.4690−4.734−4.446−4.16−4.284−4.721
218Fr → 214At(−0.01, 0)8.010−3.420−3.118−2.247−3.020−2.964
219Fr → 215At(0.011, 0)7.450−1.591−1.294−1.147−1.285−1.694
220Fr → 216At(0.057, 0.04)6.80110.8981.1972.0430.9691.620
221Fr → 217At(0.068, 0.041)6.4622.5062.8022.8682.2912.547
223Fr → 219At(0.1, 0.067)5.56247.5537.8537.8246.3217.530
203Ra → 199Rn(−0.217, 0.017)7.730−1.581−1.305−1.705−1.520−1.509
204Ra → 200Rn(−0.207, 0.004)7.640−1.282−1.007−1.419−1.239−1.244
205Ra → 201Rn(−0.207, 0.004)7.490−0.780−0.508−0.917−0.783−0.678
206Ra → 202Rn(−0.115, 0.017)7.410−0.551−0.257−0.618−0.551−0.620
208Ra → 204Rn(−0.115, 0.017)7.270−0.0720.220−0.039−0.1030.136
209Ra → 205Rn(−0.104, 0.016)7.1400.4190.6960.5780.3440.675
210Ra → 206Rn(−0.094, 0.015)7.1500.3470.6380.5010.2860.568
211Ra → 207Rn(−0.084, 0.002)7.0400.7481.0281.2060.6581.15
212Ra → 208Rn(−0.063, −0.01)7.0300.7611.0431.0710.6821.185
213Ra → 209Rn(−0.063, −0.01)6.8621.6951.9932.4991.2952.658
214Ra → 210Rn(0, 0)7.270−0.2040.0790.274−0.1960.392
215Ra → 211Rn(0, 0)8.865−3.843−3.58−3.298−4.911−2.81
217Ra → 213Rn(−0.01, 0.012)9.160−6.195−5.906−5.069−5.681−5.796
219Ra → 215Rn(−0.011, 0)8.142−3.136−2.853−2.02−2.999−1.484
220Ra → 216Rn(0, 0)7.590−1.668−1.368−1.462−1.348−1.74
221Ra → 217Rn(0.068, 0.041)6.8821.1991.4962.2901.0881.942
222Ra → 218Rn(0.079, 0.054)6.6801.7562.0531.6651.8541.572
224Ra → 220Rn(0.11, 0.068)5.7905.9576.2415.5215.6865.523
226Ra → 222Rn(0.11, 0.068)4.87011.48311.78910.69810.70210.731
  1. R, Ried; P, Paris potentials. The superscripts (emp)1 and (emp)2 stand for the improved Sahu formula and the UDL formula for both alpha and cluster decay, respectively. The experimental Qα-values and half-lives have been taken from [38].

(20)S=Aeα(ZpZ010)eβ(NpN016),

where Z0 = 102, N0 = 152, α = 0.041, and β = 0.0064 for superheavy alpha emitters.

One of the recent semi-empirical formulae for alpha decay half-life with analytic parameters is the improved Sahu formula [39], [41]. Another well-known semi-empirical formula is the universal decay law (UDL) formula [42], which has six sets of parameters for alpha decay, cluster decay, and both alpha and cluster decay with and without a fixed parameter. Here, the UDL formula for alpha decay without a fixed parameter is denoted by UDL1, and the UDL formula for both alpha and cluster decay without a fixed parameter is denoted by UDL2 [42].

The improved Sahu empirical formula is written as [39]

(21)logT1/2=aZαZdμ/Qα+bμZαZd+c+d,

where the parameters (a,b,c,d) have been determined analytically.

The UDL formula is given as

(22)logT1/2=aZαZdμ/Qα+bμZαZd(Ad1/3+Aα1/3)+c,

with the set (a=0.4065,b=0.4311,c=20.7889) for UDL1 and the set (a=0.3949,b=0.3693,c=23.7615) for UDL2.

3 Results

The model described in the previous section is now applied to obtain the alpha decay half-lives of Z = 118–121 superheavy nuclei with A ≤ 300 isotopes. With the exception of 275,276,277118 isotopes, most of the daughter nuclei have spherical shape. The maximum value of the quadruple deformation parameter of the other isotopes is β2=0.086, and we considered these isotopes as spherical nuclei in the calculations. The deformation parameters of the daughter nuclei have been taken from [43]. Because of the unknown value of the total angular momentum and the parity of unknown superheavy nuclei, the angular momentum of the alpha particle is taken as zero in the calculations.

In order to test the adopted model for the calculation of the unknown superheavy nuclei, the alpha decay half-lives of 23 isotopes of Fr and 19 isotopes of Ra nuclei were calculated. The minimum orbital angular momentum of the alpha particle, lmin, was determined based on the spin-parity selection rule [30].

In Table 1, the alpha decay half-lives of Fr and Ra isotopes are listed. T1/2(R), T1/2(P), T1/2(emp)1, and T1/2(emp)2 are the calculated half-lives with the Ried potential, the Paris potential, the improved Sahu formula, and the UDL formula for both alpha and cluster decay (20), respectively. Qα(exp) and T1/2(exp), respectively, are the experimental Q-values and half-lives, which have been adopted from the website of [38]. The pre-formation probability was considered as S = 1 in the calculations. The obtained results show reasonable agreement of the calculated half-lives with the experimental data. Figure 1 displays the comparison between the data calculated with the Ried and Paris potentials and the experimental data. Using the Paris potential gives larger values of the half-lives comaped to those obtained using the Ried potential. However, this difference lies in the range 0.26–0.31 in the logarithm of half-lives for both the isotopes of both Fr and Ra nuclei. Furthermore, in most of cases the obtained data using the Paris potential is closer to the experimental data. In general, the good agreement between the calculated half-lives and experimental data reveals the applicability of the adopted theoretical model for the prediction of the alpha decay half-lives of the heavier nuclei.

Figure 1: logT1/2$\log{T_{1/2}}$ for isotopes of (a) Fr and (b) Ra parent nuclei. The circle, triangle, and star denote logT1/2(I)R$\log T_{1/2}^{(\text{I})R}$, logT1/2(II)P$\log T_{1/2}^{(\text{II})P}$, and logT1/2(exp)$\log T_{1/2}^{(\text{exp})}$, respectively.
Figure 1:

logT1/2 for isotopes of (a) Fr and (b) Ra parent nuclei. The circle, triangle, and star denote logT1/2(I)R, logT1/2(II)P, and logT1/2(exp), respectively.

The calculated alpha decay half-lives for 279,280,281118 isotopes are given in Table 2. The superscripts (I) and (II) denote spherical and deformed cases, respectively. The upper and lower data were obtained with the Paris and the Ried-M3Y nucleon-nucleon interaction potentials, respectively. The theoretical Q-values were extracted from the WS4 mass table [44], which have been determined through the macroscopic-microscopic method. The alpha particle pre-formation probability was assumed as 1 in the calculations. The superscripts (emp)1, (emp)2, and (emp)3 stand for the improved Sahu formula, the UDL formula for alpha decay, and the UDL formula for both alpha and cluster decay, respectively.

Table 2:

Alpha decay half-lives of deformed superheavy nuclei.

Alpha decayQα(MeV)logT1/2(I)logT1/2(II)logT1/2(emp)1logT1/2(emp)2logT1/2(emp)3
279118 → 27511613.78−6.11−6.28−8.25−6.89−6.0
−6.38−6.60
280118 → 27611613.71−3.0−3.18−6.46−3.74−2.94
−3.28−3.45
281118 → 27711613.76−3.02−3.19−8.14−3.76−2.96
−3.30−3.47
  1. The superscripts (I) and (II) denote the calculated half-lives considering spherical and deformed daughter nuclei, respectively. The upper and lower half-lives were calculated with the Paris and Ried potentials, respectively. The deformation parameters of the deformed daughter nuclei are 275116: (β2=0.174,β4=0.05); 276116: (β2=0.186,β4=0.061); 277116: (β2=0.186,β4=0.074) [43]. The Qα-values were determined from the WS4 mass table [44].

The obtained results show the small effect of the inclusion of nuclear deformation on the alpha decay half-life, i.e. about 0.2 in logarithm of the half-life. Similarly, a small variation in the results, about 0.3, is observed for the Paris and Ried M3Y nucleon-nucleon potentials. The calculated half-lives are closer to those obtained from the UDL formula.

In Table 3, the calculated half-lives with the assumption of spherical daughter nuclei are listed. The superscripts I, II, and III denote the calculated half-life with the double-folding potential with setting S = 1, using (19) (with data of Table 1 of [39]) and (20) empirical formulas for the alpha pre-formation probability. P and R stand for the Paris and Ried-M3Y nucleon-nucleon potentials. The same empirical formulas as in Table 2 have been used for the calculation of the alpha decay half-lives. It is worth noting that the calculated half-lives of 294118 (294Og) with the Ried and Paris potentials with S = 1 (logT1/2(I)R = −3.15 and logT1/2(I)P= −2.87 in Table 3) are in good agreement with the experimental data logT1/2(exp)= −3.161 [38], which reveals the satisfactory performance of the adopted theoretical model.

Table 3:

Predicted alpha decay half-lives of superheavy nuclei.

Alpha decayQα(MeV)logT1/2(I)RlogT1/2(I)PlogT1/2(II)PlogT1/2(III)PlogT1/2(emp)1logT1/2(emp)2logT1/2(emp)3
282118 → 27811613.49−6.42−6.15−3.88−4.69−6.15−6.94−6.05
283118 → 27911613.33−6.13−5.92−5.09−4.47−7.32−6.65−5.76
284118 → 28011613.23−5.96−5.69−3.46−4.26−5.75−6.48−5.59
285118 → 28111613.07−5.66−5.40−4.47−3.97−6.77−6.18−5.30
286118 → 28211612.92−5.39−5.11−2.93−3.69−5.25−5.90−5.02
287118 → 28311612.80−5.16−4.88−3.86−3.46−6.19−5.67−4.80
288118 → 28411612.62−4.80−4.53−2.40−3.10−4.75−5.32−4.45
289118 → 28511612.59−4.76−4.48−3.36−3.03−5.71−5.27−4.41
290118 → 28611612.60−4.79−4.51−2.43−3.05−4.77−5.31−4.44
291118 → 28711612.42−4.43−4.15−2.93−2.66−5.30−4.95−4.09
292118 → 28811612.24−4.06−3.79−1.75−2.27−4.12−4.57−3.72
293118 → 28911612.24−4.07−3.80−2.48−2.24−4.85−4.59−3.74
294118 → 29011611.82−3.15−2.87−0.88−1.28−3.30−3.66−2.84
295118 → 29111611.90−3.35−3.07−1.66−1.43−4.06−3.86−3.03
296118 → 29211611.75−3.03−2.75−0.80−1.05−3.21−3.54−2.71
297118 → 29311612.10−3.87−3.55−2.04−1.79−4.41−4.35−3.50
298118 → 29411612.18−4.01−3.73−1.83−1.92−4.19−4.54−3.68
299118 → 29511612.05−3.76−3.47−1.86−1.58−4.22−4.27−3.42
300118 → 29611611.96−3.55−3.28−1.42−1.31−3.79−4.09−3.23
282119 → 27811714.0−7.05−6.78−4.65−5.28−6.90−7.61−6.67
283119 → 27911713.76−6.63−6.37−4.32−4.89−6.60−7.19−6.26
284119 → 28011713.57−6.30−6.03−3.95−4.57−6.24−6.85−5.93
285119 → 28111713.61−6.39−6.12−4.05−4.67−6.34−6.94−6.02
286119 → 28211713.43−6.08−5.80−3.76−4.37−6.06−6.62−5.70
287119 → 28311713.28−5.80−5.51−3.42−4.08−5.76−6.34−5.44
288119 → 28411713.23−5.76−5.44−3.44−4.01−5.77−6.26−5.36
289119 → 28511713.16−5.60−5.31−3.20−3.87−5.54−6.14−5.24
290119 → 28611713.07−5.44−5.21−3.26−3.76−5.54−5.98−5.08
291119 → 28711713.05−5.41−5.13−3.0−3.66−5.33−5.96−5.05
292119 → 28811712.90−5.13−4.85−2.95−3.35−5.29−5.67−4.77
293119 → 28911712.72−4.77−4.50−2.34−2.97−4.71−5.32−4.43
294119 → 29011712.73−4.81−4.53−2.67−2.97−5.02−5.36−4.46
295119 → 29111712.76−4.88−4.61−2.44−3.0−4.78−5.44−4.54
296119 → 29211712.48−4.32−4.04−2.22−2.39−4.59−4.86−3.98
297119 → 29311712.42−4.20−3.92−1.73−2.22−4.11−4.75−3.87
298119 → 29411712.71−4.82−4.55−2.78−2.78−5.11−5.38−4.48
299119 → 29511712.76−4.92−4.66−2.45−2.83−4.77−5.50−4.59
300119 → 29611712.57−4.54−4.28−2.56−2.38−4.90−5.12−4.22
285120 → 28111813.89−6.61−6.34−5.95−4.87−8.25−7.19−6.24
286120 → 28211814.03−6.88−6.59−4.29−5.14−6.58−7.46−6.50
287120 → 28311813.85−6.57−6.29−5.80−4.84−8.11−7.15−6.20
288120 → 28411813.73−6.37−6.08−3.83−4.64−6.15−6.94−6.0
289120 → 28511813.71−6.34−6.07−5.48−4.62−7.79−6.92−5.97
290120 → 28611813.70−6.34−6.07−3.86−4.61−6.16−6.92−5.97
291120 → 28711813.51−6.0−5.72−5.04−4.26−7.36−6.58−5.63
292120 → 28811813.47−5.93−5.66−3.51−4.17−5.82−6.52−5.58
293120 → 28911813.40−5.82−5.55−4.77−4.03−7.09−6.40−5.46
294120 → 29011813.24−5.53−5.25−3.14−3.71−5.47−6.10−5.17
295120 → 29111813.27−5.59−5.31−4.44−3.73−6.77−6.18−5.24
296120 → 29211813.34−5.74−5.47−3.41−3.85−5.72−6.33−5.39
297120 → 29311813.14−5.37−5.09−4.13−3.43−6.46−5.95−5.02
298120 → 29411813.01−5.17−4.85−2.83−3.13−5.18−5.71−4.78
299120 → 29511813.26−5.61−5.35−4.29−3.57−6.60−6.23−5.28
300120 → 29611813.32−5.75−5.47−3.50−3.63−5.81−6.36−5.41
288121 → 28411914.46−7.37−7.09−5.30−5.63−7.56−7.99−7.0
289121 → 28511914.40−7.28−7.01−5.09−5.55−7.36−7.90−6.91
290121 → 28611914.42−7.34−7.06−5.31−5.59−7.56−7.96−6.96
291121 → 28711914.40−7.36−7.03−5.10−5.56−7.35−7.94−6.94
292121 → 28811914.31−7.16−6.90−5.19−5.41−7.45−7.80−6.80
293121 → 28911914.1−6.81−6.54−4.59−5.04−6.86−7.44−6.45
294121 → 29011914.1−6.81−6.55−4.89−5.02−7.17−7.45−6.46
295121 → 29111913.98−6.61−6.35−4.38−4.80−6.66−7.25−6.26
296121 → 29211914.01−6.67−6.42−4.80−4.82−7.08−7.32−6.33
297121 → 29311914.12−6.89−6.62−4.63−4.99−6.89−7.54−6.54
298121 → 29411913.89−6.49−6.23−4.66−4.54−6.94−7.14−6.15
299121 → 29511913.65−6.07−5.80−3.79−4.07−6.09−6.70−5.72
300121 → 29611913.81−6.67−6.39−4.42−4.55−6.87−7.30−6.32
  1. The superscripts I, II, and III denote the calculated half-lives with double-folding potential with setting S = 1, using (19) and (20) empirical formulas for alpha preformation probability. P and R stand for Paris and Ried-M3Y nucleon-nucleon potentials. The Qα-values were determined from the WS4 mass table [44].

Figure 2a–d displays the calculated half-lives logT1/2(I)P, logT1/2(II)P, logT1/2(emp)1, and logT1/2(emp)3 for Z = 118, 119, 120, and 121 alpha emitters as a function of N. These figures show the odd-even effect in logT1/2(II)P and logT1/2(emp)1, which is due to the inclusion of this effect in the pre-formation probability formula (19) and the improved Sahu formula.

Figure 2: logT1/2$\log{T_{1/2}}$ for isotopes of (a) Z = 118, (b) Z = 119, (c) Z = 120, and (d) Z = 121 parent nuclei. The circle, triangle, diamond, and star denote logT1/2(I)P$\log T_{1/2}^{(\text{I})P}$, logT1/2(II)P$\log T_{1/2}^{(\text{II})P}$, logT1/2(emp)1$\log T_{1/2}^{{{(emp)}_{1}}}$, and logT1/2(emp)3$\log T_{1/2}^{{{(emp)}_{3}}}$, respectively.
Figure 2:

logT1/2 for isotopes of (a) Z = 118, (b) Z = 119, (c) Z = 120, and (d) Z = 121 parent nuclei. The circle, triangle, diamond, and star denote logT1/2(I)P, logT1/2(II)P, logT1/2(emp)1, and logT1/2(emp)3, respectively.

As can be seen from Figure 3 and Table 3, in all cases the calculated half-lives with the Paris potential are close to those obtained with the UDL empirical formula for both alpha and cluster decay (logT1/2(emp)3). These data lie in between the half-lives calculated with the improved Sahu empirical formula and those obtained using (19) empirical formula for the alpha pre-formation probability (logT1/2(II)P).

Figure 3: Parameter r1 for isotopes of (a) Z = 118, (b) Z = 119, (c) Z = 120, and (d) Z = 121 parent nuclei.
Figure 3:

Parameter r1 for isotopes of (a) Z = 118, (b) Z = 119, (c) Z = 120, and (d) Z = 121 parent nuclei.

In order to analyse the role of the Paris and Ried potentials, (19) and (20), for the pre-formation probability in the prediction of alpha decay half-life, the parameter r1 and r2 are defined as

(23)r1=logT1/2(I)PlogT1/2(I)R,
(24)r2=logT1/2(II)PlogT1/2(III)P.

Figure 3a–d shows the variation of the parameter r1 for Z = 118, 119, 120, and 121 alpha emitters as a function of N. Using the Paris potential gives larger values of the half-lives in comparison with those obtained using the Ried potential. Generally, this discrepancy is about 0.3 in logarithm of the half-lives.

Figure 4a–d displays the variation of the parameter r2 for Z = 118, 119, 120, and 121 alpha emitters as a function of N. For even-even alpha emitters, (19) gives smaller values of the pre-formation probability and consequently larger values of half-lives in comparison with those using (20). These figures show a clear odd-even staggering, which originated from the inclusion of the odd-even effect in the alpha particle pre-formation probability formula, (19). As discussed in [37], [39], the pre-formation probability is strongly dependent on the isospin. So, the inclusion of this parameter reveals the odd-even staggering in the alpha decay half-lives.

Figure 4: Parameter r2 for isotopes of (a) Z = 118, (b) Z = 119, (c) Z = 120, and (d) Z = 121 parent nuclei.
Figure 4:

Parameter r2 for isotopes of (a) Z = 118, (b) Z = 119, (c) Z = 120, and (d) Z = 121 parent nuclei.

4 Conclusion

In this theoretical investigation, we calculated the alpha decay half-lives of 22 isotopes of Z = 118, 19 isotopes of Z = 119, 16 isotopes of Z = 120, and 13 isotopes of Z = 121 superheavy nuclei with A ≤ 300 by using the WKB semi-classical method and considering the microscopic double-folding potential for nuclear potential. Three isotopes of Z = 118 alpha emitters had noticeable deformation parameter of the daughter nuclei, β2>0.1. Therefore, for these nuclei, the deformation of the daughter nucleus was taken into account. Two parameterisations of the Ried and Paris M3Y nucleon-nucleon potentials were used in the calculation, where the Paris potential predicted ∼2 times larger values of the half-lives. In the comparison between the predicted half-lives with the improved Sahu empirical formula, the UDL empirical formula for both alpha and cluster decay, and the double-folding potential with Paris parameterisation, we found that larger values of the half-lives are obtained with the UDL formula, double-folding, and the improved Sahu formula. However, the data from the improved Sahu formula for even-even nuclei are close to those obtained using the other two formulas. The role of the inclusion of the alpha pre-formation probability in the calculations was noticeable. Moreover, in order to evaluate the theoretical model and demonstrate how this model reproduces the experimental data in the lighter mass region, the alpha decay half-lives of 23 isotopes of Fr and 19 isotopes of Ra nuclei were calculated. Good agreement between theory and experiment was observed.

In this work, for sake of the comparison between the predicted half-lives of these superheavy nuclei, two forms of the Paris and Ried M3Y potentials were employed in the calculations. However, more accurate DDM3Y effective interaction may be used in the calculation of the alpha decay half-lives in future works.

References

[1] F. Li, L. Zhu, Z.-H. Wu, X.-B. Yu, J. Su, et al. Phys. Rev. C 98, 014618 (2018).10.1103/PhysRevC.98.014618Search in Google Scholar

[2] H. C. Manjunatha, K. N. Sridhar, and N. Sowmya, Phys. Rev. C 98, 024308 (2018).10.1103/PhysRevC.98.024308Search in Google Scholar

[3] K. N. Sridhar, H. C. Manjunatha, and H. B. Ramalingam, Phys. Rev. C 98, 064605 (2018).10.1103/PhysRevC.98.064605Search in Google Scholar

[4] H. C. Manjunatha and K. N. Sridhar, Nucl. Phys. A 975, 136 (2018).10.1016/j.nuclphysa.2018.04.009Search in Google Scholar

[5] H. C. Manjunatha, Indian J. Phys. 92, 507 (2018).10.1007/s12648-017-1135-7Search in Google Scholar

[6] K. P. Santhosh, C. Nithya, H. Hassanabadi, and D. T. Akrawy, Phys. Rev. C 98, 024625 (2018).10.1103/PhysRevC.98.024625Search in Google Scholar

[7] K. P. Santhosh and C. Nithya, Phys. Rev. C 97, 064616 (2018).10.1103/PhysRevC.97.064616Search in Google Scholar

[8] Y. W. Zhao, S. Q. Guo, and H. F. Zhang, Chin. Phys. C 42, 074102 (2018).10.1088/1674-1137/42/7/074102Search in Google Scholar

[9] Y. L. Zhang and Y. Z. Wang, Phys. Rev. C 97, 014318 (2018).10.1103/PhysRevC.97.014318Search in Google Scholar

[10] P. R. Chowdhury, C. Samanta, and D. N. Basu, Phys. Rev. C 73, 014612 (2006).10.1103/PhysRevC.73.014612Search in Google Scholar

[11] C. Samanta, P. R. Chowdhury, and D. N. Basu, Nucl. Phys. A 789, 142 (2007).10.1016/j.nuclphysa.2007.04.001Search in Google Scholar

[12] D. Jian-Min, Z. Hong-Fei, W. Yan-Zhao, Z. Wei, S. Xin-Ning, et al., Chin. Phys. C 33, 633 (2009).10.1088/1674-1137/33/8/007Search in Google Scholar

[13] Z. Gao-Long and L. Xiao-Yun, Chin. Phys. C 33, 354 (2009).10.1088/1674-1137/33/5/007Search in Google Scholar

[14] Z. Di-Da, C. Bao-Qiu, and M. Zhong-Yu, Chin. Phys. C 34, 334 (2010).10.1088/1674-1137/34/3/006Search in Google Scholar

[15] K. P. Santhosh and B. Priyanka, Phys. Rev. C 87, 064611 (2013); ibid. 90, 054614 (2014).10.1103/PhysRevC.87.064611Search in Google Scholar

[16] K. P. Santhosh, A. Augustine, C. Nithya, and B. Priyanka, Nucl. Phys. A 951, 116 (2016).10.1016/j.nuclphysa.2016.03.041Search in Google Scholar

[17] E. Shin, Y. Lim, C. Hyun, and Y. Oh, Phys. Rev. C 94, 024320 (2016).10.1103/PhysRevC.94.024320Search in Google Scholar

[18] P. Mohr, Phys. Rev. C 95, 011302(R) (2017).10.1103/PhysRevC.95.011302Search in Google Scholar

[19] M. Ismail and A. Adel, Phys. Rev. C 97, 044301 (2018).10.1103/PhysRevC.97.044301Search in Google Scholar

[20] S. Guo, X. Bao, Y. Gao, J. Li, and H. Zhang, Nucl. Phys. A 934, 110 (2015).10.1016/j.nuclphysa.2014.12.001Search in Google Scholar

[21] X. J. Bao, S. Q. Guo, H. F. Zhang, and J. Q. Li, Phys. Rev. C 95, 034323 (2017).10.1103/PhysRevC.95.034323Search in Google Scholar

[22] H. C. Manjunatha, Int. J. Mod. Phys. E 25, 1650100 (2016).10.1142/S0218301316501007Search in Google Scholar

[23] H. C. Manjunatha, Int. J. Mod. Phys. E 25, 1650074 (2016).10.1142/S0218301316500749Search in Google Scholar

[24] H. C. Manjunatha and N. Sowmya, Int. J. Mod. Phys. E 27, 1850041 (2018).10.1142/S0218301318500416Search in Google Scholar

[25] H. C. Manjunatha, Nucl. Phys. A 945, 42 (2016).10.1016/j.nuclphysa.2015.09.014Search in Google Scholar

[26] H. C. Manjunatha and N. Sowmya, Nucl. Phys. A 969, 68 (2018).10.1016/j.nuclphysa.2017.09.008Search in Google Scholar

[27] H. C. Manjunatha and K. N. Sridhar, Eur. Phys. J. A 53, 156 (2017).10.1140/epja/i2017-12337-ySearch in Google Scholar

[28] H. C. Manjunatha and K. N. Sridhar, Mod. Phys. Lett. A 33, 1850096 (2018).10.1142/S0217732318500967Search in Google Scholar

[29] V. Dehghani, S. A. Alavi, and Kh. Benam, Mod. Phys. Lett. A 33, 1850080 (2018).10.1142/S0217732318500803Search in Google Scholar

[30] S. Dahmardeh, S. A. Alavi, and V. Dehghani, Nucl. Phys. A 963, 68 (2017).10.1016/j.nuclphysa.2017.04.013Search in Google Scholar

[31] G. R. Satchler, W. G. Love, Phys. Rep. 55, 183 (1979).10.1016/0370-1573(79)90081-4Search in Google Scholar

[32] C. Xu and Z. Ren, Phys. Rev. C 74, 014304 (2006).10.1103/PhysRevC.74.014304Search in Google Scholar

[33] G. Scamps, D. Lacroix, G. G. Adamian, and N. V. Antonenko, Phys. Rev. C 88, 064327 (2013).10.1103/PhysRevC.88.064327Search in Google Scholar

[34] I. I. Gontchar, D. J. Hinde, M. Dasgupta, and J. O. Newton, Phys. Rev. C 69, 024610 (2004).10.1103/PhysRevC.69.024610Search in Google Scholar

[35] M. J. Rhoades-Brown, V. E. Oberacker, M. Seiwerl, and W. Greiner, Z. Phys. A 301, 310 (1983).10.1007/BF01419514Search in Google Scholar

[36] B. Buck, A. C. Merchant, and S. M. Perez, Phys. Rev. C 51, 559 (1995).10.1103/PhysRevC.51.559Search in Google Scholar

[37] H. F. Zhang, G. Royer, Y. J. Wang, J. M. Dong, W. Zuo, et al., Phys. Rev. C 80, 057301 (2009).10.1103/PhysRevC.80.057301Search in Google Scholar

[38] Chart of nuclides. Available at: https://www.nndc.bnl.gov/. Accessed 13 December, 2018.Search in Google Scholar

[39] S. Zhang, Y. Zhang, J. Cui, and Y. Wang, Phys. Rev. C 95, 014311 (2017).10.1103/PhysRevC.95.014311Search in Google Scholar

[40] W. M. Seif, J. Phys. G: Nucl. Part. Phys. 40, 105102 (2013).10.1088/0954-3899/40/10/105102Search in Google Scholar

[41] B. Sahu, R. Paira, and B. Rath, Nucl. Phys. A 908, 40 (2013).10.1016/j.nuclphysa.2013.04.002Search in Google Scholar

[42] C. Qi, F. R. Xu, R. J. Liotta, R. Wyss, M. Y. Zhang, et al. Phys. Rev. C 80, 044326 (2009).10.1103/PhysRevC.80.044326Search in Google Scholar

[43] P. Möller, A. J. Sierk, T. Ichikawa, and H. Sagawa, Atom. Data Nucl. Data Tables 109, 1 (2016).10.1016/j.adt.2015.10.002Search in Google Scholar

[44] N. Wang, M. Liu, X. Wu, and J. Meng, Phys. Lett. B 734, 215 (2014).10.1016/j.physletb.2014.05.049Search in Google Scholar

Received: 2019-01-07
Accepted: 2019-02-21
Published Online: 2019-04-02
Published in Print: 2019-07-26

©2019 Walter de Gruyter GmbH, Berlin/Boston

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