## β-delayed proton emission branches in 43Cr

β-delayed proton emission means, a positron emitted firstly, then proton emit. so, a proton converted to a neutron and a positron, then  a proton emit. as a result, the mass number reduced by 1 from lost 2 proton and gain 1 neutron. therefore, this process should be only happened in neutron-deficient nuclei.

Chromium-43 has atomic number 24, the neutron number is 19.

it was reported that a first time observation of β-delayed 3 proton decay in 45Fe. and the same decay was discovered in 43Cr in this paper. both process was recorded by an Imaging Time Projection Chamber.

the feature of this chamber is, it can capture the photos for decay process. in the paper, they shows a clear picture of 3-protons decay. and also, the measurement is very accurate. they can found 12 events of 3 protons decay among the total 12524 events of proton decay, which is about 1044 to 1. base on this precision, they deduced the relative branching ratio to be 91.8% for 1-proton case, 8.1% for 2 protons case, and 0.096% of 3 protons case.

by the chamber, they also recorded non-proton decay events, which may come from non-decay or β-deacy. the energy of β-decay is too small to detected.

However, they use the Maximum likelihood method to deduce the decay probability of β-decay. they found that it was 12%. since 2 β-decay has not been observed or either not possible, they deduced the absolute branching ratio.

a discussion on the extreme small branching ration of 3-protons decay was presented at the end of paper.

## Historical Review on Solid Polarized Target

by Akira Masaike

this review is on “Proceedings of the 11th International workshop on Polarized Sources and Targets”

the introduction stated that using thermal polarization (brute force method) in low temperature, ~ 0.01K and high magnetic field~10T can produce proton polarization as high as 76%. another way is using dynamical method by paramagnetic materials, (was proposed by Overhauser) the coupling between electron spin and proton spin can polarize proton in higher temperature and lower magnetic field. Abragam proved that by using paramagnetic impurity can also work for non-metallic materials.

Abragam and Jeffries used $La_2 Mg_3 (NO_3)_{12} 24 H_2O$ (or called LMN), containing small percent of neodymium to polarize proton spin by dynamic nuclear polarization at 1963. but the LMN crystal is not good for inelastic reaction because of the low dilution factor ( the ratio of polarized proton to total number of nucleon ), and this produce a lot other un-wanted reactions. and also the crystal is damaged under scattering by relativistic particles.

organic materials are tested and a major breakthrough is by using butanol with water doped with porphyrexide in 1969 by Mango t al.. the polarization is 40% at 1K and 2.5T.  and also, diol with $Cr^{5+}$ were polarized to 45% at 1K and 2.5T by Glättli et al. Masaike et al. was polarized diol up to 80% at temperature lower then 0.5K. Burtanol in $^3He$ cryotat also polarized upto 67%. All these were done in 1969.

deuteron in deuterated organic material can also be polarized. the principle is called “the equal spin temperature model”

$\displaystyle P = B_I( \frac{\mu B }{ 2 k_B T_s} )$

$B_I$ is Brilluin function and $T_s$ is the nuclear spin temperature.

Spin Frozen Target is a technique that the polarized proton spin last long enough with ESR radiation. the theory was developed around 1965 by Schmugge and Jeffries and constructed by Rusell at 1971 in Rutherford laboratory.

$NH_3$ or ammonia has high dilution factor. it was polarized to 70% by doped with ethylene glycol $Cr^{5+}$ complex at 0.5K and 2.5T by Scheffler and Borghini at CERN at 1971. but ammonia has slow growth of polarization and may explode by high intensity proton irradiation at 1983 at CERN.  but later, it was overcomed by Meyer et al. at Bonn. Thanks to Meyer, ammonia becomes a popular polarized target.

High polarization of H, D and $^6Li$ in dilution refrigerator were found in Bonn around 2005. The COMPASS experiment in CERN use target of $latxe ^6LiD$ at polarization 50% at 300mK and 2.5T.

Hydrogen deuteride (HD) has the highest dilution factor and in principle, both can be polarized. the relaxation properties at 0.5K depends on ortho-para and para-ortho conversions of $latxe H_2$ and $latxe D_2$. The polarization for proton and deuteron of 60% and 14% by brute force method at 10mK and 13.5T was done by Grenoble-Orsay group at 2004.

Crystal of Naphthalene (77K) and p-tarphenyl (270K) doped with pentacene have been polarized in 0.3T by Iinuma et al. at 2000. the high temperature and low magnetic field is due to the paramagnetic excited state in pentacene and diamagnetic on ground state. the population of Zeeman  sublevels of the lowest triplet state is 12% for m=+1, 76% for m=0 and 12% for m=-1 regardless of temperature and magnetic field strength. by using ESR radiation and the “integrated solid effect”, the proton can be polarized and remain polarized after the electrons go back to ground state. 70% polarization at liquid nitrogen temperature.

## Observation of non-exponential orbital electron capture decays of hydrogen-like 140Pr and 142Pm ions

This paper presented an clear a beautiful way on measuring highly charged state decay by the Schottky Mass Spectrometry.

The synchrotron frequency is related to mass by:

$\frac{\delta f}{f } = - \frac{1}{\gamma^2} \frac{ \Delta m/q }{m/q}$

For electron capture of $^{140}_{59}Pr^{58+}$ :

$p + e^- \rightarrow n + \mu_e$

The charge state does not change. Thus the frequency different is due to the mass different between parent and daught nucleus. that give an increase in frequency by 270Hz.

While for β+ decay:

$p \rightarrow n + e^+ + \mu_e$

both the charge state and mass changed after the decay. this make the frequency decrease alot. by this mean, we can observe the decay in a very clear detail.

By using the area of the Schottky frequency peak, They can identify the number of ion inside and the charge or it. because the peak is proportional to the number of stored ions and the square of charge.

the synchrotron frequency is about 2MHz. the data is analysed by FFT. each FFT frame has bandwidth 5kHz and was collected for 128ms. in this period, the ions will have 256,000 revolutions. This set of data will be FFT analysed and plot with time.

the half life of the ion is about 3.39min, thus, the time resolution is very good to give precise measurement on decay time.

the measured decay curve has an oscillation with about 7s period. they pointed out 3 possible reason for that:

1. instability of the storage ring
2. quantum beat between 2 hyperfine structure F=1/2 and F=3/2, where the nuclear spin is 1. but they also concluded that the quantum beat frequency is still 2 large for accounting it.
3. an oscillation of neutrino mass state.
Note: since the half-life is 3.39 min, is there other way to measure the electron capture and verify the 7s oscillation??

## Production of High, Long-Lasting, Dynamic Proton Polarization by Way of Photoexcited Triplet States

This paper show a 42% of nuclear spin polarization on phenanthrene $C_{14}D_{10}$  doped in fluorene $C_{13}H_{10}$ by Dynamic Nuclear Polarization (DNP), or more specific, the Integrated Solid Effect (ISE) or Integrated Cross-Polarization (ICP), or Microwave-Induced Optical Nuclear Polarization (MIONP). they use 75GHz microwave at 1.4K.

the paper pointed out that conventional guest molecule is paramagnetic in ground state. That provided a channel for nuclear spin-relaxation and  reduce the polarization. in contrast, this paper use a paramagnetic triplet state and diamagnetic ground state. Thus, when the excitation laser is turned off, the nuclear-spin relaxation can prevented.

## Dynamic Nuclear Polarization by Electron Spin in the Photoexcited Triplet State: I. Attainment of Proton Polarization of 0.7 at 105K in Naphthalene

This paper reported an excellent detail and considerations on polarization of nuclear spin by Dynamic Nuclear Polarization (DNP) method. the polarizing sample is naphthalene with 0.018mol% of pentacene. Pentacene has a paramagnetic triplet state with population independence of external magnetic field and temperature. This paramagnetic triplet state is very suitable on DNP, since the paramagnetic state like a switch to turn on the nuclear spin relaxation, due to the state will decay to diamagnetic state.

There are 5 conditions for sample:

1. Highly polarization of electron triplet state  ( since it is the source of polarization )
2. High concentration of guest molecule ( another aspect for polarization source ) ( but too high, guest molecule cluster forms and this reduce the polarization )
3. High Inter-System-Crossing rate, which is the rate from higher excited state to the triplet state, so faster the polarization build up time.
4. Long nuclear spin-lattice relaxation time ( the nuclear spin lost rate )
5. Suitable triplet state life time and electron spin-lattice relaxation time. long enough for transfer the electron spin to nuclear spin, but not so long that nuclear spin can use the paramagnetic triplet state as a channel for spin relaxation.
On the laser:
1. the pulse width should longer than the lifetime from excited state to the triplet state, but shorter than the triplet lifetime.
2. the intensity should be very high, so, the triplet state excitation depth increase. but it is not so high to increase the stimulated emission.
3. high intensity may melt the sample.
about the microwave and field sweep:
1. the time interval should be  long and not excess the adiabatic limit.
2. the sweeping range should be cover the ESR line width.
3. the field sweep should be within the lifetime of the triplet state.
they used water as a reference for the polarization measurement. the enhancement Q is defined to be:
$Q = \left( \frac { T E}{N g} \right) / \left( \frac{ T_w E_w}{ N_w g_w } \right)$
where T is temperature, N is number of proton spin, g is receiver gain and  E is the recorded signal amplitude.
at the end of this paper, it talks about some applications.

## Dynamic Nuclear Polarization

The Dynamic Nuclear Polarization (DNP) means we has a pumping source to change the population of nuclear spin, then create a polarization. in contrast, Static Nuclear Polarization (SNP) means thermal equilibrium of nuclear state population.

the introduction of the paper gives 7 applications on polarized nuclear spin.i only list some below:

1. the angular distribution on radiations can serve as a test on the theory of nuclear interaction
2. Polarized target can be used in scatter experiment
3. obtain detail information on static and dynamic interaction between nuclear spin and its environment.
4. increase the sensitivity of NMR

this paper focus on a general system and represents them by graphs ( called chart in the paper ). the graphs are based on electron spin ½ and nuclear spin also ½.

on section II, it give out the Spin Hamiltonian and use it for the discussion on the population distribution. by that, the author used the rate equations to related the population in each state. Then, he defined the Enhancement of polarization, which is the ratio between the population with saturating radiation to the thermal thermal distribution.

on section III, it mention about the first 2 successful dynamic nuclear polarization experiments around 1953-4. one group polarized the 6Li nucleus in metallic lithium. the other group polarized the 1H in solid DPPH.

The paper gives conditions for DNP, which is coupling between nuclear spin and an unpaired electron spin. the paramagnetic environment can be archived by

1. the conduction electron in metals or metal ammonia solution
2. the donor or acceptor electrons in semi-conductor
3. paramagnetic ions in diamagnetic solid
4. paramagnetic ions in solution
6. color centers

the detection of DNP can be via:

1. NMR
2. shift of EPR frequency
3. the β asymmetry or γ anisotropy from an oriented radioisotope

## Optical Pumping

DOI : 10.1119/1.1935926

This paper is easy to read and give a very easy understanding on optical pumping. it also demonstrated an experimental setup on detecting this effect. worth to read.

i am not going to reveal the detail and the experiment on the paper this time, but i just share my understanding on this subject.

The electron’s spin is polarized by optical pumping. Photon has intrinsic spin 1, and, it can be liner polarized or circular polarized. A linear polarized photon carries 0 magnetic angular momentum, and a circular polarized photon carries ±1 magnetic angular momentum. Therefore, an absorption of a circular polarized photon will make an electron undergoes ΔJ=±1and Δm=±1 transition.

In atomic energy level, a ground state is 3S½ and the next level is 3P½ and 3P3/2, the splitting of the P state is due to spin-orbital coupling between electron spin and the magnetic field generated by the orbital motion of the electron. Due to hyperfine coupling with the nuclear spin, the sub-shell will further split up. The good quantum numbers for hyper structure are |I-J|≤ F≤I+J and -F ≤ m_F≤F. The following graph demonstrated the I=3/2. The selection rule is ΔF=±1 and Δm_F=±1.

﻿

The red line is the transition by absorbed a circular polarized photon, and the black lines are possible de-excitation. Since there are 2/3 chance for the lowest state to the higher states, then, the population will move and become unbalanced. If we set up a set of rate equations, we can find out the population of each state.

A magnetic field is not necessary for optical pumping, as the graph demonstrated. The magnetic field for optical pumping is for measuring the effect. When a magnetic field is applied, the population will unbiased to, say, m_F=+1 state. Since there is no more state for absorption of the circular polarized light, then, the medium will become transparent. If we switch the magnetic field, the population will be inverted absorption will occur, and the medium become no-transparent. By measuring the intensity of the light pass through the medium, we can observe the effect of the pumping.

we can see, if the number higher energy state is more than the number of lower energy state, the maximum state has an escape channel. Look at the graph, if we have transition from F=1 to F=2 state, the m_F=+1 can absorb a photon and go to the m_F=+2 state (red dotted line). Due to relaxation, the m_F=+2 can transit to the F=2, at 3S½ state ( the black dotted lines).

Due to the lamb shift, the S-state is always little higher than the P-state in same shell. therefore, is it not possible to polarize the electron for Zero nuclear spin.