Predictions on the alpha decay half lives of Superheavy ... · Predictions on the alpha decay half...

Predictions on the alpha decay half lives of Superheavy nuclei with Z = 113 in the range 255 ≤ A ≤ 314

K. P. Santhosh*, A. Augustine, C. Nithya and B. Priyanka School of Pure and Applied Physics, Kannur University, Swami Anandatheertha Campus, Payyanur

670327, Kerala, India

Abstract

An intense study of the alpha decay properties of the isotopes of superheavy element

Z=113 have been performed within the Coulomb and proximity potential model for deformed

nuclei (CPPMDN) within the wide range 255 ≤ A ≤ 314. The predicted alpha decay half lives

of 278

113 and 282

113 and the alpha half lives of their decay products are in good agreement

with the experimental data. 6α chains and 4α chains predicted respectively for 278

113 and 282113 are in agreement with the experimental observation. Our study shows that the isotopes

in the mass range 278 ≤ A ≤ 286 will survive fission and can be synthesized and detected in the laboratory via alpha decay. In our study, we have predicted 6α chains from 279113, 4α

chains from 286

113, 3α chains from 280,281,283

113, 2α chains from 284

113 and 1α chain from 285113. We hope that these predictions will be a guideline for future experimental

investigations.

*email: [email protected]

1. Introduction

Superheavy nuclei (SHN) and their decay studies is one of the fast developing fields

in nuclear physics. Significant theoretical and experimental investigations have been made in

the region of superheavy nuclei in predicting the existence of magic island or island of

stability [1-5]. Recently the isotopes of many superheavy elements have been synthesized

successfully through hot fusion reactions [6], performed at JINR, FLNR (Dubna) and cold

fusion reactions [7], performed at GSI (Darmstadt, Germany). The concept of cold fusion was

proposed in 1970s and realized experimentally in 1980s. In cold fusion reaction the heaviest

superheavy element so far synthesized is the isotope of Z =113 (278113) by Morita et al. in

2004 [8] and the synthesis of 278

113 is confirmed in 2012 [9]. This has been recently accepted

by IUPAC and IUPAP [10]. One of the fundamental questions in nuclear physics is about the number of possible

elements that can be found in nature or that can be produced in the laboratory. Two different approaches, that is, the hot fusion approach and the cold fusion approach were used recently

to extend the periodic table. The elements with Z = 107-112 were synthesized using the cold fusion approach. Attempts to synthesize heavier elements via cold fusion were unsuccessful

because of the limited beam time of accelerators for superheavy nuclei beyond Z = 112. First attempt to synthesize the element Z=113 by cold fusion reaction was done at velocity filter

SHIP at GSI, Darmstadt. Three experimental runs were performed altogether in the period 1998-2003, without observing a single decay chain starting from an isotope of the element

Z=113. Morita et al. [8] started the experiments to synthesize the element Z=113 at the gas

filled separator GARIS, RIKEN, using 209

Bi (70

Zn, n) reaction, in September 5, 2003 and the

first decay chain of the element had been observed in 2004, which was interpreted to start

from 278

113. In 2007, Oganessian et al. [11] were successful in producing the element 282

113

by hot fusion reaction, using 48Ca projectile on actinide target 237Np, at the Flerov Laboratory

of Nuclear Reaction (FLNR) of Joint Institute of Nuclear Research (JINR), Russia and its

alpha chains has been observed.

The superheavy nuclei decay mainly by the emission of alpha particles followed by

subsequent spontaneous fission. Studies on the characteristic alpha chains will help in the

identification of new nuclides. The phenomenon of alpha decay was discovered by

Rutherford [12, 13] in 1899 and was first described by Gamow [14] in 1928 using the idea of

quantum tunneling through the potential barrier. Extensive experimental [15-23] and theoretical works [24-37] have been performed in order to understand the formation of

superheavy nuclei and their alpha decay half lives. The formation of superheavy nuclei can be successfully explained by dinuclear system (DNS) concept, in which the fusion process is

assumed as a transfer of nucleons from the light nucleus to the heavy one [38-42]. Using DNS model Adamain et al. [43] presented the calculations on the production cross sections

for the heaviest nuclei and suggested the reaction Zn68

+Bi209

for the synthesis of the isotope 279113. Based on DNS model, production cross section of superheavy nuclei Z = 112-116 in 48

Ca induced reaction is studied by Feng et al. [44]. The studies on the synthesis of

superheavy nuclei with Z = 119 and 120 [45]; and 118 [46] was done by Wang et al. within

the dinuclear system with dynamical potential energy surface model (DNS-DyPES model).

A number of works have been performed to study the properties of odd Z superheavy

nuclei [47-55]. The structure of the nuclide with Z = 105 and its alpha decay chain was

studied systematically by Long et al. [52] within the relativistic mean field approach (RMF)

in 2002. Within the density dependent cluster model, calculations on the alpha decay half

lives of the heaviest odd Z elements Rg→→113115 was done by Ren et al [31]. Using

macroscopic-microscopic model Peng et al. [51] studied alpha decay of 323 nuclei with Z ≥ 82 which includes the isotopes of odd Z elements, Z=107-115.

Theoretical studies on the alpha decay properties of Z = 113 have been done by Tai et al. [56] within the frame work of density dependent cluster model (DDCM) with

renormalized RM3Y nucleon – nucleon interactions (RM3Y) [57] and by Dong et al. [58]

using cluster model and generalized liquid drop model (GLDM).

The intention of our present work is to compare the alpha decay half lives and

spontaneous fission half lives of various isotopes of the superheavy element Z = 113 and to

predict the decay modes, using the Coulomb and proximity potential model for deformed

nuclei (CPPMDN) [59], which is an extension of Coulomb and proximity potential model

(CPPM), proposed by Santhosh et al. [60]. Our previous works on the decay properties of

heavy and superheavy nuclei [61-67] has revealed the success and applicability of CPPMDN

formalism in predicting the decay half lives. The agreement between experimental and

theoretical results is also discussed in detail.

The overview of the paper is as follows. In Sec 2, we briefly describe the features of

Coulomb and proximity potential model for deformed nuclei. The results and discussion on

the alpha decay properties of various isotopes of the superheavy element Z = 113 are presented in Sec 3 and a brief summary of the entire work is given in the last section.

2. The Coulomb and proximity potential model for deformed nuclei (CPPMDN)

The interacting potential between two nuclei in CPPMDN is taken as the sum of

deformed Coulomb potential, deformed two term proximity potential and centrifugal potential, for both the touching configuration and for the separated fragments. For the pre-scission

(overlap) region, simple power law interpolation as done by Shi and Swiatecki [68] has been

used. It was observed [60] that the inclusion of the proximity potential reduces the height of the

potential barrier, which agrees with the experimental result.

Shi and Swiatecki [68] were the first to use the proximity potential in an empirical manner

and later on, several theoretical groups [69-71] have used the proximity potential, quite

extensively for various studies including the fusion excitation function. The contribution of both

the internal and the external part of the barrier has been considered, in the present model, for the

penetrability calculation and the assault frequency, ν is calculated for each parent-cluster

combination which is associated with the vibration energy. However, for even A parents and for

odd A parents, Shi and Swiatecki [72] get ν empirically, unrealistic values as 1022 and 1020,

respectively.

The interacting potential barrier for two spherical nuclei is given by

2

22

21

2

)1()(

rzV

r

eZZV p

µ

+++=

llh, for 0>z (1)

Here 1Z and Z2 are the atomic numbers of the daughter and emitted cluster, ‘r’ is the distance

between fragment centres, ‘z’ is the distance between the near surfaces of the fragments, l

represents the angular momentum and µ the reduced mass. PV is the proximity potential given

by Blocki et al., [73, 74] as,

Φ

+=

b

z

CC

CCbzVp

)(4)(

21

21πγ (2)

with the nuclear surface tension coefficient,

]/)(7826.11[9517.0 22 AZN −−=γ MeV/fm2 (3)

Here N, Z and A represent the neutron, proton and mass number of the parent and Φ represents

the universal proximity potential [74] given as

( ) 7176.0/41.4 εε −−=Φ e , for ε ≥1.9475 (4)

( ) 32 05148.00169.09270.07817.1 εεεε −++−=Φ , for 0 ≤ ε ≤ 1.9475 (5)

With bz=ε , where the width (diffuseness) of the nuclear surface 1≈b fermi and the Süsmann

central radii Ci of the fragments are related to the sharp radii Ri as

−=

i

iiR

bRC

2

fm (6)

For Ri, we use semi-empirical formula in terms of mass number Ai as [73] 3/13/1

8.076.028.1−+−=iii

AAR fm (7)

The potential for the internal part (overlap region) of the barrier is given as,

( )nLLaV 00 −=

, for z < 0 (8)

where 21 22 CCzL ++= fm

and CL 20 = fm, the diameter of the parent nuclei. The constants

0a and n are determined by the smooth matching of the two potentials at the touching point.

Using the one dimensional Wentzel-Kramers-Brillouin approximation, the barrier penetrability P is given as

−−= ∫ dzQVP

b

a

)(22

exp µh

(9)

Here the mass parameter is replaced by AAmA /21=µ , where m is the nucleon mass and A1, A2

are the mass numbers of daughter and emitted cluster respectively. The turning points “a” and

“b” are determined from the equation, V (a) = V (b) = Q. The above integral can be evaluated numerically or analytically, and the half life time is given by

=

=

PT

νλ

2ln2ln2/1 (10)

where,

=

=

h

Ev2

2π

ων represent the number of assaults on the barrier per second and λ the

decay constant. Ev, the empirical vibration energy is given as [75]

( )

−+=

5.2

4exp039.0056.0 2A

QEv , for 42 ≥A (11)

Classically, the α particle is assumed to move back and forth in the nucleus and the usual way of determining the assault frequency is through the expression given by )2/( Rvelocity=ν ,

where R is the radius of the parent nuclei. As the alpha particle has wave properties, a quantum mechanical treatment is more accurate. Thus, assuming that the alpha particle vibrates in a

harmonic oscillator potential with a frequency ω, which depends on the vibration energy vE , we

can identify this frequency as the assault frequency ν given in equations (10) and (11). The Coulomb interaction between the two deformed and oriented nuclei with higher

multipole deformation included [76, 77] is taken from Ref. [78] and is given as,

∑=

+

+

++=

2,1,

2,

)0(2)0(

1

02

21

2

21 )(7

4)(

12

13

i

iiiii

C YYr

ReZZ

r

eZZV

λλλλλλλ

λ

δαββαλ

(12)

with

+= ∑

λλλ αβα )(1)(

)0(

0 iiiii YRR (13)

where 3/13/1

0 8.076.028.1 −+−= iii AAR . Here αi is the angle between the radius vector and

symmetry axis of the ith

nuclei (see Fig.1 of Ref [76]) and it is to be noted that the quadrupole

interaction term proportional to 2221ββ , is neglected because of its short-range character.

The proximity potential and the double folding potential can be considered as the two variants of the nuclear interaction [79, 38]. In the description of interaction between two fragments, the latter is found to be more effective. The proximity potential of Blocki et al., [73, 74], which describes the interaction between two pure spherically symmetric fragments, has one term based on the first approximation of the folding procedure and the two-term proximity potential of Baltz et al., (equation (11) of [80]) includes the second component as the second approximation of the more accurate folding procedure. The authors have shown that the two-

term proximity potential is in excellent agreement with the folding model for heavy ion reaction, not only in shape but also in absolute magnitude (see figure 3 of [80]). The two-term proximity

potential for interaction between a deformed and spherical nucleus is given by Baltz et al., [80] as

2/1

2

2

2/1

1

12

)(

)(

)(

)(2),(

++

++=

SRR

RR

SRR

RRRV

C

C

C

CP

α

α

α

απθ

2/1

1

2

201

1

10 )(

)(2

)()()(

)(2

)()(

++

++× S

RR

RRSS

RR

RRS

C

C

C

C εα

αεε

α

αε

(14)

where θ is the angle between the symmetry axis of the deformed nuclei and the line joining

the centers of the two interacting nuclei, and α corresponds to the angle between the radius

vector and symmetry axis of the nuclei (see Fig. 5 of Ref [80]). )(1 αR and )(2 αR are the

principal radii of curvature of the daughter nuclei, CR is the radius of the spherical cluster, S

is the distance between the surfaces along the straight line connecting the fragments, and

)(0 Sε and )(1 Sε are the one dimensional slab-on-slab function.

The barrier penetrability of α particle in a deformed nucleus is different in different directions. The averaging of penetrability over different directions is done using the equation

∫=π

θθθ0

)sin(),,(2

1dQPP l

(15)

where ),,( lθQP is the penetrability of α particle in the direction θ from the symmetry axis

for axially symmetric deformed nuclei.

3. Results and discussion

Studies on the decay properties of superheavy nuclei provide information on their

existence and stability in nature. The investigations on the half lives of different radioactive

decay play a significant role in determining the properties of superheavy nuclei. The dominant decay modes of superheavy nuclei involve alpha decay and spontaneous fission. Several theoretical models are available for calculating the alpha decay half lives as well as spontaneous fission half lives. It is seen that those nuclei with small alpha decay half lives

than the spontaneous fission half lives survive fission and thus can be detected in laboratories via alpha decay.

3.1 Alpha Decay Half lives

In the present study the alpha half lives of the isotopes of SHN with Z = 113 have

been studied within the range 255≤ A ≤314 using CPPMDN and the present values are then compared with those calculated by means of CPPM [60], Viola-Seaborg semiempirical (VSS)

relationship [81], The Universal (UNIV) curve of Poenaru et al. [82, 83] and the analytical formula of Royer [84].

The alpha decay is characterised by the energy release Qα and the corresponding life time Tα. In alpha transitions, Q value is the energy released between the ground state energy levels of the parent nuclei and ground state energy levels of the daughter nuclei and is given as,

)()( εε

α dpdp ZZkMMMQ −+∆+∆−∆=

(16)

which is positive for a given decay. Here ∆Mp, ∆Md, ∆Mα are the mass excess of the parent, daughter and alpha particle respectively. In order to calculate the Q value, the mass

excesses are taken from Ref [85, 86]. The electron screening correction [87] have been included by the term k(Zp

ε - Zd

ε), where k = 8.7eV , ε =2.517 for Z ≥ 60 and k = 13.6eV,

ε = 2.408 for Z < 60. The quadrupole (β2) and hexadecapole (β4) deformation values of the parent and daughter nuclei have been used for the calculation of alpha half lives and the

deformation values taken from Ref. [88] are used for the calculation. The well known Viola-Seaborg semi-empirical Relationship (VSS) formula for

calculating the alpha decay half lives is given by,

log

21

2110 )()(log hdcZQbaZT ++++= −

(17)

Here the half life is in seconds and the Q value is in MeV. Z is the atomic number of the

parent nucleus, a, b, c, d, hlog are adjustable parameters. The quantity hlog gives the hindrance

of alpha decay for the nuclei with odd proton and odd neutron numbers [81]. Instead of using

the original set of constants given by Viola and Seaborg [81], more recent values determined

by Sobiczewski et al. [89] has been used here. The constants are a = 1.66175, b = -8.5166,

c = -0.20228, d = -33.9069 and

==

==

==

==

=

oddNoddZfor

oddNevenZfor

evenNoddZfor

evenNevenZfor

h

,114.1

,066.1

,772.0

,0

log (18)

For calculating the decay half lives several simple and effective relationships are

available, which are obtained by fitting experimental data. Among them one of the important relationship is the UNIV curves [90-93], derived by extending a fission theory to larger mass

asymmetry. Based on the quantum mechanical tunnelling process, the relationship [94, 95] of

the disintegration constant λ, valid in both fission like and α-like theories, and the partial

decay half life T of the parent nucleus is given as,

SSPT νλ == /2ln

(19)

Here ν, S and PS are three model dependent quantities. ν is the frequency of assaults on the

barrier per second, S is the pre-formation probability of the cluster at the nuclear surface

(equal to the probability of the internal part of the barrier in a fission theory [90, 91]), and PS

is the quantum penetrability of the external potential barrier. By using the decimal logarithm equation (18) becomes,

]log)2(ln[logloglog)(log 1010101010 ν−+−−= SPsT

(20)

To derive the universal formula, the basic assumptions were that ν = constant and S

depends only on the mass number of emitted particle Ae [91, 94]. It was shown by a

macroscopic calculation of pre-formation probability [96] of many clusters from 8Be to 46Ar

that, Ae depends only upon the size of the cluster. Using a fit with experimental data for α

decay, the corresponding numerical values [91] had been obtained: sα = 0.0143153,

ν = 1022.01

s-1

. The additive constant for even-even nuclei is given as,

16917.22)]2(lnloglog[ 1010 −=+−= νeec (21)

And the decimal logarithm of the pre-formation factor is

)1(598.0log10 −−= eAS

(22)

The penetrability of an external Coulomb barrier, having the separation at the

touching configuration Ra = R = Rd + Re as the first turning point, and the second one defined

by QRZZe bed =/2

may be obtained analytically as,

])1([arccos)(22873.0log 2/1

10 rrrRZZP bedAS −−×=− µ (23)

where bt RRr /= fm

, )(2249.1 3/13/1

edt AAR += fm

and QZZR edb /43998.1=

fm.

To calculate the released energy Q, the liquid drop model radius constant r0 = 1.2249

fm and the mass tables [85, 86] are used.

Geiger and Nuttal [97] formulated the earliest law for the alpha decay half lives.

Several expressions [81, 89, 98, 99] were advanced subsequently. Royer [84] formulated the

following formula by a fitting procedure applied on a set of 373 alpha emitters with a RMS deviation of 0.42

[ ]αQ

ZZAsT

5837.1114.106.26)(log 6/1

2/110 +−−=

(24)

Here A and Z are the mass and charge numbers of the parent nuclei and Qα is the energy

released during the reaction. The following relation corresponds to a subset of 86 odd-even nuclei and a RMS deviation of

0.36

[ ]αQ

ZZAsT

592.11423.168.25)(log 6/1

2/110 +−−=

(25)

For a subset of 50 odd-odd nuclei the RMS deviation was found to be 0.35 and the formula is

given by,

[ ]αQ

ZZAsT

6971.1113.148.29)(log 6/1

2/110 +−−=

(26)

3.2 Spontaneous fission half lives

The spontaneous fission (SF) half-lives of various nuclei can be calculated by using the

semi-empirical relation given by Xu et al [100]. The equation was originally made to fit the even-even nuclei and is given as,

−−−++++= )64.1113323.0()(2exp

31

22

4

4

3

2

21021A

ZZNCZCZCACCT π

(27)

Here the constants C0 = -195.09227, C1 = 3.10156, C2 = -0.04386, C3 = 1.4030 x 10-6 and

C4 = -0.03199. In the present work we have considered only the odd mass (i.e odd-even and

odd-odd nuclei) nuclei. So instead of taking spontaneous fission half lives directly, we have

taken the average of spontaneous fission half lives of corresponding neighboring even-even

nuclei. In the case of odd-even nuclei, we took the av

sfT of two neighboring even-even nuclei

and while dealing with odd-odd nuclei, the av

sfT of four neighboring even-even nuclei was

taken.

Attempts to synthesize the superheavy element Z=113 started as early as 2003. The

isotope 278

113 was produced through 207

Np+70

Zn reaction with six consecutive alpha chains

[9]. The 282

113 nuclide was synthesized through 237

Np+48

Ca fusion reaction and consequently

its alpha decay chains were observed [101]. Various isotopes of the element Z=113 namely 283113 and 284113 have been observed in the decay chains of isotopes of Z=115 and the

isotopes 285

113, 286

113 have been observed in the decay chains of isotopes of Z=117 [102]. In

the present paper we compare the alpha decay half lives and spontaneous fission half lives of

various isotopes of Z=113 in order to find the mode of decay of these nuclides, concentrating mainly on the recently synthesized 278, 282113 isotopes and then theses were compared with

experimental data. The comparison of spontaneous fission half lives and alpha decay half lives calculated within our model and the predictions on the decay chains are given in Table

1. The comparison of the present values with other theoretical models is also shown.

In Table 1 the first column denotes the parent and daughter nuclei. Column 2 gives

experimental Q values of these isotopes taken from Ref [9, 101]. The spontaneous fission half

lives of the isotopes under study evaluated using the phenomenological formula of Xu et al. is

given in column 3. Experimental alpha decay half lives obtained from [9, 101] are arranged

in column 4. Column 5 shows the alpha decay half lives of these isotopes calculated using

CPPMDN formalism. The alpha half life calculations using CPPM are given in column 6. In

CPPMDN the nucleus-nucleus interaction potential is calculated using equation (14),

while in CPPM (spherical case) the potential is calculated using equation (2). On comparing the alpha decay half lives calculated within both these formalisms we can see

that the alpha half lives decrease with the inclusion of deformation values. Within our fission

model the pre-formation probability, S [103, 104] can be calculated as the penetrability

of the internal part (overlap region) of the barrier given as

)exp( KS −=

(28)

Where

dzQVKa

∫ −=0

)(22

µh

(29)

here, a is the inner turning point and is defined as QaV =)( and 0=z represents the

touching configuration. The VSS, analytical formula of Royer and UNIV have also been

used for determining the alpha decay half lives and are given in columns 7, 8 and 9

respectively. The last column represents the mode of decay of isotopes under study. From the

table, it is clear that, by comparing the SF half lives with the alpha decay half lives we can

predict a 6α chains from the isotope 278

113, which agrees well with the experimental observation. Experimentally it was shown that after the 6

thα chain, the isotope

254Md shows

electron capture (bε = 100%) [105] and thereafter the daughter isotope 254

Fm will undergo alpha decay. The same result has been predicted within CPPMDN. In the case of 282113, it

can be clearly seen that the alpha decay half lives computed within CPPMDN closely agrees with the experimental values. By comparing the SF half lives calculated using the semi-

empirical relation given by Xu et al. with the alpha decay half lives we can predict α chains from the isotope, but for a more accurate prediction on the decay mode, we have used the

values given by Smolanczuk et al. [106, 107], in which the spontaneous fission half lives of

even-even nuclei with Z=104-114 has analyzed in a multidimensional deformation space, in a

dynamical approach without any adjustable parameters. Using these values, the average

spontaneous fission half lives were calculated, and on comparing the alpha decay half lives with the corresponding spontaneous fission half lives we can predict 4α chains for the isotope 282

113, which matches very well with the experimental result. So by using our formalism, even though there is a one order difference in alpha decay half lives for some of the isotopes

under study, the predictions on the alpha decay half lives and decay modes of the

experimentally synthesized 278

113 and 282

113 go hand in hand with the experimental results.

Thus we extended our work to predict the alpha decay half lives and mode of decay of 58

more isotopes of Z = 113, ranging from 255 ≤ A ≤ 314.

Figures 1-15 represents the entire work. We have plotted log10T1/2 against the mass number of the parent nuclei. All the calculations done within the various theoretical models

are shown. It is to be noted that the decay half lives evaluated by using VSS formula, UNIV and the analytical formula of Royer match well with our theoretical calculations.

Figure 1-3 shows the plot of log10T1/2 versus mass number for the parent nuclei 255-266113 and their decay products. By comparing the alpha decay half lives with the

corresponding spontaneous fission half lives, it can be clearly seen that none of these isotopes will survive fission. In figure 4, the plots of isotopes 267-270113 are shown. We can see that the

isotopes 267-269

113 will not survive fission, whereas the isotope 270

113 will survive fission and

shows full alpha chain within CPPMDN. Figures 5 and 6, shows the plot for the isotopes 271-278

113, which include the experimentally synthesized SHN 278

113. It is clear from the

figure that all these isotopes will survive fission and show full alpha chain within CPPMDN.

But in the case of 278113, it was seen that after the 6th chain the daughter isotope, 254Md,

undergoes electron capture. Even though the isotopes 270-277

113 decay by emitting alpha

particles, they are hard to detect in laboratory because of their small decay times (for e.g., α

2/1T = 3.059x10-8s for 270113 and α2/1T = 1.320x10-8s for 271113). The calculations done for the

experimentally synthesized 278113 is shown in figure 6(d). Experimental alpha decay values

have been represented as scattered points in the figure. Plot for the isotopes 279-282

113 are shown in figure 7. It is seen that the isotope 279113 shows full alpha chain within CPPMDN.

But after the 6th

alpha chain the isotope 255

Md shows electron capture (bε = 92%) [105] and thereafter the daughter isotope 255Fm will undergo alpha decay. The isotopes 280, 281113 will

survive fission and shows 3α chains by comparing the alpha decay half lives with the spontaneous fission half lives of Xu et al. In the case of 282113, we got 4α chains as

mentioned earlier. The half lives for these isotopes are in millisecond range (in the case of 280

113 α2/1T = 7.131 x 10

-4s, for

281113 α

2/1T = 1.635 x 10-3

s and for 282

113 α2/1T = 4.873 x 10

-3s)

and hence can be synthesized and detected via alpha decay in laboratory. Figure 7(d)

represents the plot of experimentally synthesized 282113. The scattered points in the figure

represent experimental alpha decay values. The average spontaneous fission values given by

Xu et al. and Smolanczuk et al. are also shown. Figure 8 depicts the decay properties of

isotopes 283-286

113. From the figure it is clear that the isotopes 283-285

113 will survive fission

and 3α, 2α and 1α chains can be predicted respectively from the isotopes 283

113, 284

113 and 285

113. These isotopes can be detected in laboratory through alpha decay because of their

longer alpha half lives. It is to be noted that our theoretical predictions on the alpha decay half lives and decay modes of the nuclei 283113 and 284113 matches well with the

experimental values of these isotopes, which were obtained as the decay products of 288

115 and 287115 respectively [108], and the comparison between experimental and theoretical

results are given in detail in Table 1 of our previous work Ref [61]. Similarly the isotopes 285113 and 286113 were observed as the decay products of the isotopes 293117 and 294117

isotopes respectively [23]. It is seen that the alpha decay half lives calculated within CPPMDN is in good agreement with the experimental results. In the case of 286113, for a

better matching with experimental decay modes, we have adopted the spontaneous fission

values given in [106, 107]. 4α chains can be predicted from the isotope by comparing the

alpha decay half lives with the spontaneous fission half lives and it is evident that the

predictions on the decay modes of the isotope is same as the experimental results. The

comparison between experimental and theoretical values of alpha decay half lives and decay

modes are given in Table 1 of Ref [63]. Figures 9-15 represents the plots for the isotopes 287

≤A ≤ 314. We can see that none of these isotopes will survive fission and it is hard to observe

them in laboratories. Thus the nuclei within the range 278 ≤ A ≤ 286 were found to have

relatively long alpha decay half-lives and can be detected in laboratory. These predictions are

included in Table II and Table III. Table II shows the comparison of the spontaneous fission

half lives with the alpha decay half lives for the nuclei 279-281,283,284113 and Table III shows

the same for 285,286

113 nuclei. We have also included the predictions on the decay modes of

these isotopes within CPPMDN, which will be helpful in future experimental investigations. The pictorial representation of alpha decay chains of predicted isotopes are shown in figure

16. We hope that our present study, which predicts the mode of decay of various isotopes

of Z = 113 within a wide range 255 ≤ A ≤ 314, by comparing the alpha decay half lives and the corresponding spontaneous fission half lives of respective isotopes, may open up new

lines in experimental investigations.

4. Conclusion

In the present paper we have shown the theoretical predictions on the alpha decay half

lives of various isotopes of the element Z = 113, within the Coulomb and proximity potential

for the deformed nuclei (CPPMDN). We could successfully reproduce the alpha half lives

and decay chains for the experimentally synthesized isotopes 278

113 and 282

113. Hence an

extensive study has been done for predicting the alpha decay half lives and decay chains of

all the other isotopes in this region. Through our study we understood that isotopes of

Z = 113 within the range 278 ≤ A ≤ 286 will survive fission and can be synthesized and

detected in laboratories. We have predicted 6α chains from 279

113, 3α chains from 280,281,283113, 2α chain from 284113, 1α chain from 285113 and 4α chains from 286113. We hope

that these predictions will be a guideline for the future experimental investigations.

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255 251 247 243 239 235 231 227 223 219 215 211

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

256 252 248 244 240 236 232 228 224 220 216 212-45

-40

-35

-30

-25

-20

-15

-10

-5

0

257 253 249 245 241 237 233 229 225 221 217 213-45

-40

-35

-30

-25

-20

-15

-10

-5

0

258 254 250 246 242 238 234 230 226 222 218 214

-35

-30

-25

-20

-15

-10

-5

0

5

(a)

255113

(b)

256113

Mass number of the parent nuclei

log

10(T

1/2)

(c)

257113

(d)

258113

SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

Fig 1: The comparison of the calculated alpha decay half-lives with the spontaneous fission

half-lives for the isotopes 255-258

113.

259 255 251 247 243 239 235 231 227 223 219 215

-35

-30

-25

-20

-15

-10

-5

0

260 256 252 248 244 240 236 232 228 224 220 216

-30

-25

-20

-15

-10

-5

0

5

261 257 253 249 245 241 237 233 229 225 221 217

-30

-25

-20

-15

-10

-5

0

5

262 258 254 250 246 242 238 234 230 226 222 218-25

-20

-15

-10

-5

0

5

10

(a)

259113

SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

(b)

260113

(c)

261113

(d)

262113

log

10(T

1/2)



half-lives for the isotopes 259-262113.

263 259 255 251 247 243 239 235 231 227 223 219-25

-20

-15

-10

-5

0

5

10

264 260 256 252 248 244 240 236 232 228 224 220

-21

-14

-7

0

7

14

265 261 257 253 249 245 241 237 233 229 225 221

-15

-10

-5

0

5

10

15

20

266 262 258 254 250 246 242 238 234 230 226 222

-15

-10

-5

0

5

10

15

20

(a) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

263113

(b)

264113

(c)

265113


(d)

266113

log

10(T

1/2)



113.

267 263 259 255 251 247 243 239 235 231 227 223

-15

-10

-5

0

5

10

15

20

268 264 260 256 252 248 244 240 236 232 228 224

-10

-5

0

5

10

15

20

25

269 265 261 257 253 249 245 241 237 233 229 225

-10

-5

0

5

10

15

20

25

270 266 262 258 254 250 246 242 238 234 230 226-10

-5

0

5

10

15

20

25

(a) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

267113

(b)

268113


(c)

269113

(d)

270113

log

10(T

1/2)



271 267 263 259 255 251 247 243 239 235 231 227-10

-5

0

5

10

15

20

25

272 268 264 260 256 252 248 244 240 236 232 228-10

-5

0

5

10

15

20

25

273 269 265 261 257 253 249 245 241 237 233 229

-10

-5

0

5

10

15

20

25

274 270 266 262 258 254 250 246 242 238 234 230

-10

-5

0

5

10

15

20

25

30

(a) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

271113

(b)

272113

(c)

273113

log

10(T

1/2)


(d)

274113



113.

275 271 267 263 259 255 251 247 243 239 235 231

-10

-5

0

5

10

15

20

25

30

276 272 268 264 260 256 252 248 244 240 236 232

-10

-5

0

5

10

15

20

25

30

277 273 269 265 261 257 253 249 245 241 237 233

-10

-5

0

5

10

15

20

25

30

278 274 270 266 262 258 254 250 246 242 238 234-10

-5

0

5

10

15

20

25

30

(a)

275113


(b)

276113

(c)

277113

log

10(T

1/2)

(d) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

Expt.

278113



279 275 271 267 263 259 255 251 247 243 239 235-10

-5

0

5

10

15

20

25

30

280 276 272 268 264 260 256 252 248 244 240 236-10

-5

0

5

10

15

20

25

30

281 277 273 269 265 261 257 253 249 245 241 237-10

-5

0

5

10

15

20

25

30

282 278 274 270 266 262 258 254 250 246 242 238

-5

0

5

10

15

20

25

(a)

279113

(b)

280113

281113


SF [100]

SF [106, 107]

CPPM

CPPMDN

VSS

UNIV

ROYER

Expt.

(d)

282113

log

10(T

1/2)

(c)



283 279 275 271 267 263 259 255 251 247 243 239-5

0

5

10

15

20

25

284 280 276 272 268 264 260 256 252 248 244 240-5

0

5

10

15

20

25

30

285 281 277 273 269 265 261 257 253 249 245 241

-5

0

5

10

15

20

25

30

35

286 282 278 274 270 266 262 258 254 250 246 242

-5

0

5

10

15

20

25

(a)

log

10(T

1/2)

283113

(b)

284113

(c)


285113

(d)

286113

SF [100]

SF [106, 107]

CPPM

CPPMDN

VSS

UNIV

ROYER



287 283 279 275 271 267 263 259 255 251 247 243-10

-5

0

5

10

15

20

25

288 284 280 276 272 268 264 260 256 252 248 244-10

-5

0

5

10

15

20

25

30

289 285 281 277 273 269 265 261 257 253 249 245

-10

-5

0

5

10

15

20

25

30

290 286 282 278 274 270 266 262 258 254 250 246

-10

-5

0

5

10

15

20

25

30

35

(a) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

287113

(b)

288113

(c)

289113

(d)

290113


log

10(T

1/2)



113.

291 287 283 279 275 271 267 263 259 255 251 247

-10

0

10

20

30

292 288 284 280 276 272 268 264 260 256 252 248

-10

0

10

20

30

293 289 285 281 277 273 269 265 261 257 253 249-20

-10

0

10

20

30

40

294 290 286 282 278 274 270 266 262 258 254 250-20

-10

0

10

20

30

40

(a)

291113

SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

(b)

292113

(c)

293113


log

10(T

1/2)

(d)

294113



113.

295 291 287 283 279 275 271 267 263 259 255 251

-20

-10

0

10

20

30

40

296 292 288 284 280 276 272 268 264 260 256 252

-20

-10

0

10

20

30

40

50

297 293 289 285 281 277 273 269 265 261 257 253-40

-20

0

20

40

60

80

298 294 290 286 282 278 274 270 266 262 258 254-40

-20

0

20

40

60

80

100

(a)295

113(b)

296113

(c)297

113


log

10(T

1/2)

(d) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

298113



299 295 291 287 283 279 275 271 267 263 259 255

-30

0

30

60

90

120

150

300 296 292 288 284 280 276 272 268 264 260 256-60

-30

0

30

60

90

120

301 297 293 289 285 281 277 273 269 265 261 257

-40

-20

0

20

40

60

80

100

302 298 294 290 286 282 278 274 270 266 262 258

-40

-20

0

20

40

60

80

100

(a)299

113

SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

(b)300

113


log

10(T

1/2)

(c)301

113

(d)302

113



303 299 295 291 287 283 279 275 271 267 263 259-60

-40

-20

0

20

40

60

80

100

120

304 300 296 292 288 284 280 276 272 268 264 260-60

-40

-20

0

20

40

60

80

100

120

305 301 297 293 289 285 281 277 273 269 265 261

-60

-30

0

30

60

90

120

150

306 302 298 294 290 286 282 278 274 270 266 262

-60

-30

0

30

60

90

120

150

(a) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

303113

(b)304

113

(c)305

113


log

10(T

1/2)

(d)306

113



113.

307 303 299 295 291 287 283 279 275 271 267 263

-50

0

50

100

150

308 304 300 296 292 288 284 280 276 272 268 264

-50

0

50

100

150

200

309 305 301 297 293 289 285 281 277 273 269 265-100

-50

0

50

100

150

200

250

310 306 302 298 294 290 286 282 278 274 270 266

-60

0

60

120

180

240

300

360

(a)

307113

SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

(b)308

113

(c)

309113

log

10(T

1/2)

(d)

310113




311 307 303 299 295 291 287 283 279 275 271-100

-50

0

50

100

312 308 304 300 296 292 288 284 280 276 272-100

-50

0

50

100

150

313 309 305 301 297 293 289 285 281 277 273

-100

-50

0

50

100

150

200

314 310 306 302 298 294 290 286 282 278

-65

0

65

130

195

260

325

(a)311

113

(b)312

113

(c)313

113


log

10(T

1/2)

(d) SF [100]

CPPM

CPPMDN

VSS

UNIV

ROYER

314113

Fig15: The comparison of the calculated alpha decay half-lives with the spontaneous fission


Fig 16: Predicted decay chains for 279-281113 and 283-285113 isotopes within CPPMDN. The

calculated Q values and decay times are shown.

Table I: The comparison of the calculated alpha decay half lives with the spontaneous fission half

lives for the isotopes 278,282113 and its decay products. av

SFT is calculated using Ref [100].

*Q value computed using experimental mass excess [85]

# av

SFT calculated using Ref [106, 107]

Parent

Nuclei

αQ (Exp)

MeV

av

SFT

(S)

α2/1T

Mode

of

Decay Expt CPPMDN CPPM VSS UNIV Royer

278113 11.82±0.06 3.831x10

1 0.667ms

01.0

01.002.0 −

+ms 03.0

02.008.0−

+ms 11.0

03.031.0 −+

ms 004.0

003.001.0 −+

ms 05.0

03.012.0 −+

ms α1

274Rg 10.65±0.06 2.853x10-1 9.97ms 89.0

61.094.1−+

ms 01.8

45.539.17 −

+ms 49.19

63.1333.46 −

+ ms 61.0

43.050.1 −+

ms 44.10

12.787.22 −+

ms α2

270Mt 10.26±0.07 4.686x10

-2 444ms 40.11

49.1875.19 −

+ms 31.25

87.1546.43−

+ms

20.59

42.3870.111−

+ms 88.1

24.169.3 −+

ms 98.30

48.1963.53 −+

ms α3

266Bh 9.39±0.06 1.811x10-1 5.26s 03.0

02.006.0−

+s 86.1

34.137.3 −+

s 25.3

42.244.6 −+

s 09.0

08.020.0 −+

s 10.2

52.183.3 −+

s α4

262Db

8.63±0.06 6.941x10

0 126s

89.0

51.034.1 −+

s 28.127

40.7750.201 −+

s 30.167

40.10580.290 −

+s 26.5

33.328.9 −+

s 20.134

70.8120.213 −+

s α5

258Lr

8.66±0.06 1.603x10

3 3.78s 05.0

03.007.0 −+

s 03.16

86.915.26 −+

s 39.24

52.1573.43 −+

s 86.0

55.057.1−

+s 03.16

87.927.26 −+

s α6

254Md - - - - - - - - *EC

282113 10.63±0.08 3.023x10

-1# 134

2973+−

ms 31.12

31.74.18 −+

ms 6.54

3.329.80−+

ms 8.131

815.214 −+

ms 745.1

738.34.5 −+

ms 7.73

71.430.110 −

+ ms α1

278Rg 10.69±0.08 8.388x100# 5.7

7.12.4 +−

ms 03.1

72.16.2 −

+ms 5.4

6.76.11 −+

ms 6.13

8.217.36 −

+ ms 369.0

585.00.1 −+

ms 9.5

8.91.15 −

+ ms α2

274Mt 10.0±1.10 1.221x10

3# 81.0

17.044.0 +−

s 24.75

023.0023. −+

s 9.700

210.021.0 −+

s 44.10

55.055.0−+

s 94.23

149.0015.0 −+

ms 35.817

252.025.0 −+

s α3

270Bh 8.93±0.08 3.329x10

3#

292

2861+

−s 56.2

84.452.5−+

s 8.43

2.8326.94−+

s 1.72

1.13170.163 −+

s 806.1

258.315.4−+

s 4.98

6.9100.104 −

+s α4

266Db

8.265* 2.121x10

3# - 86.14s 3694.00s 4970.00s

131.50

3798.00s SF

Table II: Predictions on the mode of decay of 279-281113 and 283,284113 superheavy nuclei and their

decay products by comparing the alpha half lives and the corresponding spontaneous fission half lives. av

SFT is calculated

using Ref [100].

Parent

Nuclei

αQ (Cal)

MeV

av

SFT

(S)

T1/2(s) Mode

of

Decay CPPMDN CPPM VSS UNIV Royer

279113 11.611 6.676x10

1 6.074x10

-5 2.591x10

-4 4.118x10

-4 3.229x10

-5 1.185x10

-4 α1

275Rg 11.790 4.715x10-1 2.844x10-6 2.257x10-5 4.483x10-5 4.084x10-6 1.245x10-5 α2

271Mt 9.958 6.248x10

-2 1.913x10

-2 3.251x10

-1 3.282x10

-1 2.168x10

-2 9.354x10

-2 α3

267Bh 9.287 1.957x10

-1 1.619x10

-1 7.180x10

0 5.931x10

0 3.892x10

-1 1.712x10

0 α4

263Db 8.885 6.947x10

0 2.369x10

-1 2.664x10

1 2.013x10

1 1.395x10

0 5.894x10

0 α5

259Lr 8.630 1.540x103 1.228x10-1 3.357x101 2.484x101 1.873x100 7.395x100 α6

255Md 7.952 1.641x10

6 1.751x10

0 1.532x10

3 8.534x10

2 6.863x10

1 2.688x10

2 *EC

280113 11.221 7.832x10

1 7.131x10

-4 2.290x10

-3 7.295x10

-3 2.273x10

-4 3.211x10

-3 α1

276Rg 11.540 5.148x10-1 1.386x10-5 8.296x10-5 3.513x10-4 1.311x10-5 1.129x10-4 α2

272Mt 10.398 5.440x10

-2 1.042x10

-3 1.651x10

-2 4.879x10

-2 1.539x10

-3 2.031x10

-2 α3

268Bh 9.077 1.295x10

-1 1.057x10

0 3.243x10

1 5.676x10

1 1.584x10

0 3.631x10

1 SF

281113 11.061 8.988x101 1.635x10-3 5.742x10-3 8.066x10-3 5.120x10-4 2.154x10-3 α1

277Rg 11.290 5.580x10

-1 5.684x10

-5 3.306x10

-4 5.942x10

-4 4.401x10

-5 1.532x10

-4 α2

273Mt 10.658 4.632x10

-2 2.646x10

-4 3.106x10

-3 4.891x10

-3 3.456x10

-4 1.251x10

-3 α3

269Bh 8.617 6.328x10

-2 3.963x10

1 1.221x10

3 7.805x10

2 4.380 x10

1 2.132x10

2 SF

283113 10.541 2.348x10

1 3.209x10

-2 1.383x10

-1 1.660x10

-1 8.709x10

-3 4.117x10

-2 α1

279Rg 10.570 1.351x10

-1 5.420x10

-3 2.401x10

-2 3.372x10

-2 1.956x10

-3 8.131x10

-3 α2

275Mt 10.268 9.492x10

-3 4.107x10

-3 3.420x10

-2 4.832x10

-2 2.910x10

-3 1.149x10

-2 α3

271Bh 9.537 7.582x10-3 5.983x10-2 9.673x10-1 1.097x100 6.409x10-2 2.640x10-1 SF

284113 10.281 1.234x10

1 1.265x10

-1 7.427x10

-1 1.802x10

0 3.933x10

-2 9.883x10

-1 α1

280Rg 10.250 7.076x10

-2 5.307x10

-2 1.852x10

-1 5.107x10

-1 1.215x10

-2 2.329x10

-1 α2

276Mt 10.048 4.952x10-3 2.425x10-2 1.415x10-1 4.098x10-1 1.035x10-2 1.683x10-1 SF

Table III: Predictions on the mode of decay of 285,286

113 superheavy nuclei and their decay products

by comparing the alpha half lives and the corresponding spontaneous fission half lives. av

SFT is

calculated using Ref [100].

# av

SFT calculated using Ref [106, 107]

Parent

Nuclei

αQ (Cal)

MeV

av

SFT

(S)

T1/2(s) Mode

of

Decay CPPMDN CPPM VSS UNIV Royer

285113 10.091 1.186x10

0 5.381x10

-1 2.617x10

0 2.740x10

0 1.221x10

-1 6.309x10

-1 α1

281Rg 9.820 6.390x10

-3 7.702x10

-1 3.408x10

0 3.602x10

0 1.675x10

-1 8.147x10

-1 SF

286113 9.831 6.259x10

4# 3.335x10

0 1.577x10

1 3.319x10

1 6.196x10

-1 2.055x10

1 α1

282Rg 9.560 3.258x10

2# 3.948x10

0 2.147x10

1 4.538x10

1 8.862x10

-1 2.619x10

1 α2

278Mt 9.518 1.236x10

0# 1.048x10

0 5.371x10

0 1.283x10

1 2.736x10

-1 6.210x10

0 α3

274Bh 8.977 1.018x101# 6.230x100 5.656x101 1.165x102 2.545x100 6.120x101 α4

270Db 8.365 1.335x101# 8.365x101 1.361x103 2.240x103 5.106x101 1.367x103 SF

Predictions on the alpha decay half lives of Superheavy ... · Predictions on the alpha decay half...

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