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No measurement on a single decay reveals its angular momentum
(identifying the multi-pole nature of the g ). source Need to take many measurements on a sample counting the occurrence of Eg -decays as a function of angle
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We know, for fixed mj the radiation is given by the Poynting vector
where Same for E and M multipoles
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60Co’s -decay to 60Ni is accompanied by two rapid gamma emissions
in succession (lifetimes of ~10-12 sec, make them seem simultaneous) Obviously cascading to its ground state 60Co ½ = 5.26 years 1g7/2 1g9/2 2p1/2 1f 5/2 2p3/2 1f 7/2 8 1d3/2 4 2s1/2 2 1d5/2 6 28 1p1/2 2 1p3/2 4 1s1/2 2 b- I = ? 2506 keV 4 I = 2+ 1333 keV I = 0+ GROUND 60Ni
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would lead you to expect
60Co’s -decay to 60Ni is accompanied by two rapid gamma emissions in succession (lifetimes of ~10-12 sec, make them seem simultaneous) 60Co Assuming (trying) different values for I1 would lead you to expect ½ = 5.26 years b- I = ? 2506 keV I1 = 0 I = 2+ 1333 keV I1 = 3 I = 0+ GROUND I1 = 4 60Ni
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unless special steps taken to orient nuclei
Jintial mj1 = -j1, -j1+1, …, j1-1, j1 mj2 = -j2, -j2+1, …, j2-1, j2 Jfinal unless special steps taken to orient nuclei the various mj states are equally populated and mj Sjmj = constant
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Jintial = 1 Jfinal = 0 0 0 1 0 mj1 = -1, 0, +1 mj2 = 0 minitial
mfinal 0 0 1 0 With the three mj1 states equally populated: Isotropic! independent of .
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B-field Ji = 1 Jf = 0 Jf = 0 mi = -1 mi = -1, 0, +1 mi = 0 mi = +1
E+E E E-E Jf = 0 mf = 0 Jf = 0 mf = 0 E = mB but to compare atomic to nuclear splitting look at one Bohr magneton and the nuclear magneton:
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minitial = +1 However applying a strong magnetic field
to a nuclear system at low temperature can exploit the Boltzmann distribution At kT<<mB the nuclear spins are aligned with the external B-field minitial = +1
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At T << B nuclear spins tend to be aligned with the external B
Yielding, for example for mi=+1 /2 3/2 2
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Description of Nuclear Polarization
Polarization
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Low temperature Nuclear Orientation
At high temperatures ( 1 K !) occupation of the nuclear energy levels are equal. At lower temperatures (100 mK) the lower energy levels are preferentially occupied. For this a 3He:4He dilution refrigerator is widely used.
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Measurement of temperature
Resistance thermometry 3He Melting curve thermometry Nuclear orientation thermometry
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Nuclear orientation is detected by
the temperature-dependent change in the pattern of emitted radiation from appropriate nuclei. most easily measured for the radiation that exits the cryostat walls of the cooling chamber (for low energy and radiation the detectors need to be inside the cryostat). For 60Co, even at 1 K radiation, the pattern of radiation is uniform in all directions.
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This is most easily detected by a g-detector
At lower temperatures the radiation pattern becomes distorted This is most easily detected by a g-detector aligned with the sample axis though frequently an azimuthal detector is also used. An external magnetic field may be needed to sweep out magnetic domains, ensuring all of the target nuclei are correctly aligned.
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Nuclear orientation schematic for the example of 60Co.
Nuclear orientation schematic for the example of 60Co.
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Ultra Low Temperature Thermometry
For work below 0.3 K 3He/4He dilution refrigerator Capable of reaching ultra low temperatures down to 10 mK. The equilibrium concentration of 3He/4He is temperature and pressure dependent. The vapor pressure of 3He is higher than 4He Manipulating the 3He/4He concentration (by pumping) can control the temperature. Similar to evaporation techniques in your refrigerator.
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The production of low temperatures Dilution refrigeration
Evaporation refrigeration using liquid 3He (T~0.3 to 0.5 Kelvin) Dilution refrigeration continuous refrigeration to low temperatures but low cooling power 3He 3He 4He 4He 3He + 4He mixture at T>0.8 K Phase Separation Driven by osmotic pressure differences when temperature is low enough ~0.8 K Dilution and Cooling Driving temperatures lower T0.01 K
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Pumping chamber draws 3He out of solution Still return line “Sink”
3He/4Ne mixture Mixing chamber
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High magnetic fields and superconducting magnets
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Angular Correlation Technique Ef -counter Ei-counter Ji g1
source Ji g1 Useful when there is a cascade of successive radiations J g2 Jf After the 1st transition the orientation of atoms is no longer random i.e., not all mj-values for the 2nd transition are equally probable!
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Ji g1 J g2 Jf mj = J, J-1, … -(J-1), -J mj = -1
As a simple example, consider the special case where Ji = Jf = 0 with an intermediate state of J. g1 J g2 For the initial transition to the intermediate nuclear state mj = J, J-1, … -(J-1), -J are equally likely. Jf Suppose 1 carries off angular momentum 1. It must leave the intermediate nuclear state with mj = -1. ?? Since mf can only = 0, it follows 2 = mj = -1 Nature’s randomly selected 1st step, fixes the nature of the 2nd step.
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^ J = 1 mj = -1, 0, +1 Ji g1 J g2 Jf Ef -counter Ei-counter
For example suppose J = 1 mj = -1, 0, +1 Ji g1 J g2 The 1st transition emits 1 leaving the nucleus in one state of mj. Jf Positioning a detector effectively fixes the z-axis, by selecting a direction! When the Ei-counter registers a hit it is selecting p1 as the z-axis. ^ Ef -counter Any it detects can’t be from a ~sin2 distribution, only the ~ 1 + cos2. Ei-counter source The Ei-counter preferentially selects out the m=1 decays!
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With 1 = 0, the Yjm=Yj0 transition is not even detected.
The remaining (equally likely) cases m = 1 have been selected out. The distribution resulting from these two contributions of coincident radiation So if Ji=0, J=1, Jf=0 (the dipole transition Krane uses as an example) or if J=2
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