# 物理代写|核物理代写nuclear physics代考|PHYS585

## 物理代写|核物理代写nuclear physics代考|Parity Violation

$\beta$-decay exhibits a further remarkable property. It violates conservation of parity.
Parity violation in the weak interactions was first proposed by Chen-Ning Yan and Tsung-Dao Lee in 1956 [59] and verified in 1957 by Chien-Shiung Wu [60]. She performed a seminal experiment on the decay of radioactive ${ }{27}^{60} \mathrm{Co}$ (cobalt), whose ground state has spin-parity $5^{+}$into an excited state of ${ }{27}^{60} \mathrm{Ni}$, with spin-parity $4^{+}$
$${ }{27}^{60} \mathrm{Co}\left(5^{+}\right) \rightarrow{ }{28}^{60} \mathrm{Ni}^*\left(4^{+}\right)+e^{-}+\bar{v} .$$
This is an allowed Gamow-Teller transition. The nickel nucleus returns to its ground state, emitting two $\gamma$-rays. The cobalt sample was placed in a strong magnetic field in order to align the direction of the nuclear spin and cooled to almost absolute zero so that thermal fluctuations did not destroy the spin polarization. From the properties of the electromagnetic interactions responsible for the emission of the $\gamma$-rays, the correlation between the angular distribution of the $\gamma$-rays and the direction of the spin of the ${ }_{27}^{60} \mathrm{Co}$ nucleus was known. The measurement of this angular distribution was used to determine the degree of polarization of the nuclear spin, which was found to be around $60 \%$.

The rate of emission of electrons in the direction of the magnetic field was measured and the direction of the magnetic field was reversed in order to measure the rate of emission in the direction opposite to that of the magnetic field. What was observed was an excess of electrons (around 20\%) emitted in the opposite direction to the magnetic field (i.e. opposite to the direction of polarization of the nuclear spin), as shown schematically in diagram (a) of Fig. 7.5. After a few minutes this excess disappeared, owing to the warming of the sample so that thermal fluctuations erased the spin polarization.

## 物理代写|核物理代写nuclear physics代考|Double Beta-Decay

It can sometimes happen that a particular nuclide, with atomic number $Z$, is stable against either $\beta^{-}$- or $\beta^{+}$-decay, but its binding energy is less than the binding energy of the isobar with atomic number $(Z+2)$ or exceeds it by less than $1.56 \mathrm{MeV}$ (twice the mass difference between a neutron and a proton plus an electron). In that case it is energetically possible for the nuclide to undergo double $\beta$-decay:
$${ }Z^A{P} \rightarrow \underset{Z+2}{A}{D}+2 e^{-}+2 \bar{v}$$ emitting two electrons and two antineutrinos. An example of this is ${ }{52}^{130} \mathrm{Te}$, which has a binding energy of $1095.94 \mathrm{MeV}$, whereas the binding energies of its neighbouring isobars are smaller than this and by an amount exceeding the rest energy difference $\left(m_n-m_p-m_e\right) c^2=0.782 \mathrm{MeV}$. This nuclide is therefore stable against single $\beta$-decay. On the other hand the binding energy of ${ }_{54}^{130} \mathrm{Xe}$ is $1096.91 \mathrm{MeV}$ so that the double $\beta$-decay $${ }{52}^{130} \mathrm{Te} \rightarrow{ }{54}^{130} \mathrm{Xe}+2 e^{-}+2 \bar{v}$$
is energetically possible. However, the decay rate for such processes is very much suppressed so the half-life is extremely long, making these events extremely difficult (but not impossible) to observe. The half-life of ${ }{52}^{130} \mathrm{Te}$ is $7 \times 10^{20}$ years. The relative abundance of ${ }{52}^{130} \mathrm{Te}$ is $33.8 \%$, so that in a sample of 1 gram of naturally occurring tellurium there will be on average about 2 double $\beta$-decay events per year.

Another scenario that can give rise to double $\beta$-decay occurs when single $\beta$ decay is energetically possible but highly suppressed because the transition is forbidden. An example of this is ${ }{20}^{48} \mathrm{Ca}$, whose ground state has spin-parity $0^{+}$, and whose binding energy is $415.99 \mathrm{MeV}$. It is just energetically possible for this nuclide to decay to ${ }{21}^{48} \mathrm{Sc}$ (scandium) with binding energy $415.48 \mathrm{MeV}$ (lower than that of ${ }{20}^{48} \mathrm{Ca}$, but by an amount less than $0.782 \mathrm{MeV}$ ), but the ground state of ${ }{21}^{48} \mathrm{Sc}$ has spinparity $6^{+}$, so such a decay is 5 th forbidden. There are two excited states of ${ }{21}^{48} \mathrm{Sc}$ to which ${ }{20}^{48} \mathrm{Ca}$ can also decay and these have spin-parities $5^{+}$and $4^{+}$. This means that such single $\beta$-decays are at least 3rd forbidden. On the other hand, the ground state of ${ }{22}^{48} \mathrm{Ti}$ has spin-parity $0^{+}$, and a binding energy $418.69 \mathrm{MeV}$. Double $\beta$-decay of ${ }{20}^{48} \mathrm{Ca}$ is an allowed Fermi transition and is energetically permitted. This double $\beta$ decay has been observed by the NEMO experiment [61] and the measured half-life is $6 \times 10^{19}$ years.

## 物理代写|核物理代写nuclear physics代考|Parity Violation

$\beta$-decay 表现出更显着的特性。它违反了宇称守恒。

$$27^{60} \mathrm{Co}\left(5^{+}\right) \rightarrow 28^{60} \mathrm{Ni}^*\left(4^{+}\right)+e^{-}+\bar{v}$$

(a) 所示。几分钟后，由于样品升温，这种过量消失了，因此热波动消除了自旋极化。

## 物理代写|核物理代写nuclear physics代考|Double Beta-Decay

$$Z^A P \rightarrow \underset{Z+2}{A} D+2 e^{-}+2 \bar{v}$$

$$52^{130} \mathrm{Te} \rightarrow 54^{130} \mathrm{Xe}+2 e^{-}+2 \bar{v}$$

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