Proceedings of the DAE Symp. on Nucl. Phys. 58 (2013) 154
Semi empirical Formula for neutrinoless double beta decay
M. K. Preethi Rajan 1, R. K. Biju 2 and K. P. Santhosh 3 * 1Department of Physics, Payyanur College, Payyanur-670327, INDIA 2Department of Physics, Pazhassi Raja N S S College, Mattanur- 670702, INDIA 3School of Pure and Applied Physics, Kannur University, Payyanur Campus, Payyanur-670327, INDIA . * email: [email protected]
Introduction 2 − 1 ( 0 ) 2 〈 m ν 〉 = (1) T 1 / 2 G 0 ν M 0 ν Double beta decay is a radioactive decay m e process where a nucleus releases two beta rays as Where G0ν is the phase space factor for this single process. Here two neutrons in the nucleus decay mode,
operator, the NMEs can be also expressed as a Semi empirical formula sum of products of two-body transition densities In the standard scenario, when 0 νββ decay (TBTDs) and matrix elements of the two-body process occurs by exchange of light Majorana transition operators for two-particle states. We neutrinos between two nucleons inside the have seen a Z -1/3 dependence of nuclear matrix nucleus, and in the presence of left handed weak element and a new formula is obtained by interactions, the life time expression can be making least-squares fit to the data taking from written as a product of three factors, given as the ref [4] and is given as,
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Proceedings of the DAE Symp. on Nucl. Phys. 58 (2013) 155
)0( = − 3/1 + − 3/2 + − 3/3 experimental values and other nuclear models M 0ν aZ bZ cZ − 3/4 − 3/5 and is found that the present value= 3.883156, + dZ + eZ + f (3) QRPA = 3.578705, Truncated Shell The constants are, Model=3.2091 and NSM=4.062309. It is found a = -9.49274E +6, b= 6.65787E +7, from the values that the present formula is better c = -2.33125E +8, d= 4.07518E +8, than NSM and slight greater than QRPA and e = -2.84509E +8, f = 540571.09879. Truncated Shell Model, but the present formula is very simple for computation and the other two Results discussion and conclusion models are complicated.
Table 1 shows the comparison of computed Table 1: The Q values, M and half lives of half-life time with the experimental data for 0V double beta decay with the present formula and neutrino less double beta decay. It is found from is compared with the experimental values. the table that our present formula predictions are Isotope Q value M Half life in good agreement with the experimental values. 0V (KeV) Present Expt . In the present calculation
(y Te 2527 2.53 1.32E27 >2.8E24 -15 50 136 Xe 2458 2.68 1.21E27 >4.5E23 40 x10 150
ν Nd 3371 1.37 8.88E26 >1.8E22 o 30 160 G Gd 1730 3.09 1.50E27 >1.3E21 20
10
0 60 )
0 500 1000 1500 2000 2500 -1 3 50 Ref [3]
ZQ (MeV) (y Present -1 5 40 3 Fig. 1 The plot of phase space factor versus ZQ 30 x1 0
for various isotopes undergoing neutrinoless ν o 20
double beta decay G
10 80
70 0
) 0ν double beta decay -1 60 P d M o S n P t Zr X e S e C d G d C a (y G e T e N d S m T e N d 9 6 8 2 4 8 7 6 1 1 0
50 1 0 0 1 2 4 1 9 8 1 3 6 1 1 6 1 6 0 1 3 0 1 5 0 1 5 4 1 2 8 1 4 8 -15 40 x10 30 ν
Fig. 3 The plot connecting the comparison of 0 20 G computed phase space factor with those obtained 10 from Ref [3] for neutrinoless double beta decay. 0 0 1x10 6 2x10 6 3x10 6 4x10 6 5x10 6 References 2 6 Z Q (MeV) [1] J Suhonen et al, Phys.Rep. 300, 123 (1998)
2 6 [2] E Caurier et al, Phys.Rev.Let,77,1954(1996) Fig. 2 The plot of phase space factor versus Z Q [3] R G H Robertson,arXiv:1301.1323v1 (2013) for various isotopes undergoing neutrinoless [4] V A Rodin et al,Nucl.Phys A 766, 107 (2006) double beta decay
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