- #1
Leonardo Machado
- 56
- 2
Hi everyone.
I'm currently trying to master the use of the formula for nuclear masses from MYERS AND SWIATECKI (1969), https://www.sciencedirect.com/science/article/pii/0003491669902024.
$$
E=[-a_1+J\delta^2+0.5(K\epsilon^2-2L\epsilon \delta^2 +M\delta^4)]A+c_2 Z^2 A^{1/3}
+[a_2(1+2\epsilon)+Q \tau^2]A^{2/3}+a_3A^{1/3} \\
+c_1\frac{Z^2}{A^{1/3}} (1-\epsilon+0.5\tau A^{-1/3}) -2c_2 Z^2 A^{1/3} -c_3 \frac{Z^2}{A} -c_4 \frac{Z^{4/3}}{A^{1/3}},
$$
where
$$
I=(A-2Z)/A,\\
\delta=(I+\frac{3}{8} \frac{c1}{Q} \frac{Z^2}{A^{5/3}})/(1+\frac{9}{4}\frac{J}{Q} A^{-1/3}),\\
\epsilon=\frac{1}{K}(-2a_2A{-1/3}+L\delta^2+c_1\frac{Z^2}{A^{4/3}}),\\
\tau=(\frac{3}{2}\frac{J}{Q}\delta-\frac{1}{4}\frac{c_1}{Q}\frac{Z^2}{A^{4/3}}).
$$
and the coefficients are ( in MeV):
$$
a_1=15.677, \\
a_2=18.56, \\
a_3=9.34, \\
J=28.062, \\
K=294.8, \\
L=123.53, \\
M=2.673, \\
Q=16,04, \\
c_1=0.717, \\
c_2=0.0001479, \\
c_3=0.84, \\
c_4=0.5475.
$$
The point is, i can't obtain the correct Z that minimizes $$M(A,Z)=Z m_p + (A-Z) m_n + E(A,Z)$$. I'm obtaining Z=24 because M(56,24)=55.948365... and M(56,26)=55.948670..
Does anyone use this formula and know if there is any detail that I'm not seen?
*This formula only works to even-even nuclei.
I'm currently trying to master the use of the formula for nuclear masses from MYERS AND SWIATECKI (1969), https://www.sciencedirect.com/science/article/pii/0003491669902024.
$$
E=[-a_1+J\delta^2+0.5(K\epsilon^2-2L\epsilon \delta^2 +M\delta^4)]A+c_2 Z^2 A^{1/3}
+[a_2(1+2\epsilon)+Q \tau^2]A^{2/3}+a_3A^{1/3} \\
+c_1\frac{Z^2}{A^{1/3}} (1-\epsilon+0.5\tau A^{-1/3}) -2c_2 Z^2 A^{1/3} -c_3 \frac{Z^2}{A} -c_4 \frac{Z^{4/3}}{A^{1/3}},
$$
where
$$
I=(A-2Z)/A,\\
\delta=(I+\frac{3}{8} \frac{c1}{Q} \frac{Z^2}{A^{5/3}})/(1+\frac{9}{4}\frac{J}{Q} A^{-1/3}),\\
\epsilon=\frac{1}{K}(-2a_2A{-1/3}+L\delta^2+c_1\frac{Z^2}{A^{4/3}}),\\
\tau=(\frac{3}{2}\frac{J}{Q}\delta-\frac{1}{4}\frac{c_1}{Q}\frac{Z^2}{A^{4/3}}).
$$
and the coefficients are ( in MeV):
$$
a_1=15.677, \\
a_2=18.56, \\
a_3=9.34, \\
J=28.062, \\
K=294.8, \\
L=123.53, \\
M=2.673, \\
Q=16,04, \\
c_1=0.717, \\
c_2=0.0001479, \\
c_3=0.84, \\
c_4=0.5475.
$$
The point is, i can't obtain the correct Z that minimizes $$M(A,Z)=Z m_p + (A-Z) m_n + E(A,Z)$$. I'm obtaining Z=24 because M(56,24)=55.948365... and M(56,26)=55.948670..
Does anyone use this formula and know if there is any detail that I'm not seen?
*This formula only works to even-even nuclei.