The operation of gamma ray lasers (gasers) are studied. It is assumed that the nuclear isomers mentioned in previously published papers have inherent limitations. It is further assumed that the judicious use of Bormann effect or the application of the total external reflection of low energy gamma radiation at grazing angle of incidence may permit the use of a gaser crystal sufficiently long to achieve observable stimulated emission. It is suggested that a long lived 0(+) isomer decaying by low energy gamma ray emission to a short lived 2(+) excited nuclear state would be an attractive gaser candidate. It is also suggested that the nuclear isomer be incorporated in a matrix of refractory material having an electrostatic field gradient whose principal axis lies along the length of the medium. This results in the preferential transmission of electric quadrupole radiation along the length of the medium

Jha, S.

English

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PFINAL TECHNICAL REPORT
NASA Grant No. NSG 3091
15 Jan 1977 - 31 May 1979
PASA,-04-163482) NUCLEAR ISUMER SUITABLE
	 W80-30727
.FUR GAMMA RAY LASER Final Toc-:hnical Report,
1S Jan. 1977 - 31 flay 1979 (Cinci.tivati
Uuiv . ) 16 p HC A02/IMF" AJ 1 	 CSCL 20R	 Unclas
OJ/36 28487
NUCLEAR ISOMER SSUITABLE FOR GAMMARAY LASER
Shacheenatha Jha
Principal Investigator
Univex'sity of Cincinnati
Cincinnati, Ohio
	 45221
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r
 Introduction:
The necessary conditions for the successful operation of Gamma-ray Lasers
(Gasers) are .
a) population inversion
b) minimum electronic absorption of the gamma ray in the medium
c) recoilless emission of the gamma rays to permit stimulated emission
d) absence of nuclear recoilless absorption to avoid line broadening
e) a sufficiently long medium
(%A)
Recent review articles have described the difficulties which have to be overcome
in successfully realizing a gamma-ray laser. The state of our knowledge of
nuclear structure and of the interaction of the nucleus with its environment was
insufficient to allow the early pioneers to foresee many of the problems3'4.
Perhaps the most difficult of the originally perceived problems, how to
obtain a density of inverted states sufficient to achieve lasing, has not been
solved, There is, however, no known fundamental limitation to achieving high
densities; and man's continuing effort to make his sources more powerful may
someday solve the intensity problems.
In this paper we assume that the nuclear isomers mentioned in published
papers have inherent limitations. We assume also that the judicious use of
Bormann effect or the application of the total external reflection of low-energy
gamma radiation at grazing angle of incidence may permit the use of a GASER cry-
stal sufficiently long to achieve observable stimulated emission.
1. V.A. Bush and R.N. Kuzmin, Sor., Phys. Usp 17, 942, (1975).
2. G.C. Baldwin and R.R. Khokhlov, Phys. Today, 28, 32, (1975).
3. B.V. Chirikov, Sov. Physiks JETP 17, 1355, 1963.
4. W. Vali and V. Vale, Proc. IEEE 51, 182, 1963.
5. M.N. Yakimenko, Sov. Phys. 17, 651, 1975.
9.
We suggest that a long-livVd 6+ isomer decaying by low energy gamma-ray
emission to a short-lived 2+ excited nuclear state would be an attractive
caser candidate, We suggest that the nuclear isomer be incorporated In a matrix
of refractory material having an (EF(;) electrostatic field gradient whose princi-
pal axis lies along the length of the medium. This will. result in the prefer-
ential transmission of electric quadrupole radiation (some fraction of it,
rus coil- less) along the len '-:0 of the medium.
General Consideration of the, Nuclear Isomer and the Matrix:
When dealing with atomic nuclei, the achievement of a population inversion
is a simple task. 114 m In (half-life 50 days, spin and parity 5 +) has been sug-
gested for a long time. The energy of the isomeric transition (5 	 1) is
191.6 keV. It may be pointed out that tho energy of the transition is especially
critical. The parasitic absorption by the atomic electrons falls off as the
energy of the gamma ray increases, while the cross-section for the stimulated
emission is proportional to the inverse square of the energy of the gamilin ray
-	
Thn latter consider,	 a201) . 	 consideration leads one to select 	 low energy isomeric
transition. There is another reason for selecting low energy transitions.
Success in achieving laser action with atomic nuclei. critically hinges on the
probability of recoilless emission of the gamma ray. The recoilless fraction f
is given by
21c'
f a exp
where E 
Y2 12 Mc 2 is the recoil energy and 0 is the Debye temperature of the matrix.
D
The recoil-froo fraction f Is nvg]Ag1b'JV fol' g,1111111a rzly L1*411ISitiO118 Of e111!1'Vy
91.eater than about 15) keV.
	
Gatim►a radiation emitted between nuclear level 2 	 0 or 0	 2 actually
involves transitions from or to the sublevels w - + 2 , +1 and 0. If the matrix
- 2 -
3in which the nuclear isomer is incorporated is non-cubic and more especially, the
electrostatic field gradient q is axially symmetric, then the sublevela split
and the three transitions are shifted in energy as shown in figure 1. Tine
angular distribution of the gamma radiation with respect to the symmetry axis
is given by
W(0) - 3W Cos 4 0) for A m - + 2
W(0) - 'k(1 - 3 Cos2 0 + G Cos 40) for A m
W(0) - 3(cos2 0 - Cos 40 for A m - 0
These radiation patterns are shown :Lit figure 2 and clearly demonstrate that if one has
a 0+ or 2+
 isomer incorporated in a non-cultic crystal, which has a symmetric
electrostatic .field gradient whose principal axis lies along the long axis of
the crystal, then the A m - + 1 component is preferentially emitted alone the
crystal, axis. The cross section for stimulated emission is ;Likewise greatest
along the long axis of the crystal.. If the energy of the gamma ray is not too
high and the Debye-temperature of the matrix is high enough, there may exist a.
large fraction of recoilless ganuna -ray photons. Mien one of these photon inter-
acts with another nucleus in the 0+ or 2+ isomeric state, then a stimulated.
emission will occur. However, only the A m - +lphotons travelling along the
axis of the crystal., will have an energy match with the A m - +1substates. The
gamma rays arising from the other two sublevel transitions would emerge prefer-
entially perpendicular to the axis of the crystal.
These ideas are based on Mossbauer absorption experiments for 2+ -)- 0+ tran-
sitions. The absorption of the recoilless photon in a tungsten disulfide (W S2)
single crystal (hexagonal close packed) which has an EEG with principal axis
along the c-axis at each tungstennucleus gave the results shown in fig. 3a. Only
a single component A m - + 1, is resonantly aborbed when the recoilless photon
is incident travelling along the c axis. A similar result is shown in fig. 3b
- 3
for the 2+ _> 0+ transition in 178 lif where the gntiva ray travellin g
 
alon g the
axis of the hafnium metal single crystal was resonantly absorbed. In both
cases, the results confirmed that only the A in - + I transition is absorbed
parallel to the syttimetry axis. So it is inferred that the A m w + I component
of the 2+ to- 0 transition from an isomer incorporated in a matrix with a
symmetric electrostatic field gradient along the long axis of the crystal will
be emitted preferentially along the long axis of the crystal.
Filamentary iklignment of the Nuclear Isomers:
It was recognized by tile inventors of the gamma ray laser concept that the
alignment of the active atoms along a single axis could solve the problem of
the non-exIsterice of mirrors with which to form a cavity. Whisker crystals, were
suggested as a possible materials configuration.
The idea of a whisker configuration can be combined with the allisotropic
distribution of the A iii - + I component of 0+ <•> 2+ quadrupole radiation. What
is rerjukred to do this is an electric field gradient along the whisker filament
and the crystal structure of tile filament to be symmetric about tile whisker axis.
The concept is shown in figure 4.
Preferred Level Arrangement for time Nuclear Isomer:
As we have indicated, a long-lived isomer, having a spin sequence of levels
+	 J.	
+	
+2 4 0* or 0 ► 2 in a host having an axially symmetric field-gradient, will
provide a directed propogation of tile gamma radiation. Additional considerations
favor the situation 0
	
2	 i.e. the isomeric state should be the 0 state, the
lower state should be the 2+
 state, and both states should be above the ground
state. Whenever the ground state takes part in the isomeric transition, one can-
not avoid the recoilless absorption of the gamma ray, causing an excitation from
the ground to the isomeric state. This results in the broadening of the gamma-
ray width and a loss of gamma-rays from the beam direction. Any broadening of
- 4 -
h"__ .-, __	 -
5the gamma-ray linewidth reduces the cross-section for the stimulated emission ao,
a0 In rT 1+a
Here A is the wavelength of the radiation.
C total. width
T = the effective lifetime of the transition. If the two levels are both
unstable, having a mean life t opper - to and tlower = t t , then
T # 1/( 1/tu + 1/tk)
R branching ratio of the isomeric transition
a - internal conversion coefficient
f - recoilless fraction.
When the transition does not involve the ground state, there will be no nuclear
absorption of the recoilless gamma rays and consequently no broadening of the
linewidth on this account. In addition, there will be n~ broadening of the 0+
level due to stochastic field gradients or a distribution of magnetic fields at
the nucleus, since the 0+ state has no moment. The only factor still causing the
broadening of the 0+ state will be the inhomogeneous isomer shift. As pointed
out by Baldwin and khokhlov, the additional broadening, for nuclear lifetimes
shorter than 10-6 sec., is negligible and the product (rT) is essentially unity.
It may be clearly sta°^d that we have examined only the integral spin possi-
bilities. We do not rule out nuclear ;isomers Involving half-integral. spins. The
question as to whether 0+ isomers exist which decay with a mean-life of 10 -6 sec
or less and having a transition energy of tens of keV can only be answered by
studies in nuclear isomerism. In what follows a short review is given of the
occurrence of isomerism in even A nuclei. It is quite possible that odd-odd
nuclei will provide a rich variety of isomers, but our knowledge of such nuclei
- 5 -
6
is rather limited. We shall therefore confine our attention to even-even nuclei.
Isomers in Even-Even Nuclei:
Among the even-even nuclei are to be found some (rare earth and actinide
nuclei) which are permanently deformed. This low-lying spectra of such nucleides
are given in fig. 5. They consist of a rotational band built on the 0+ ground
state, and higher up, rotational bands Built on the beta vibrational 0+ and
gamma-vibrational 2+ states. ?.^he transitions among the levels of these bands are
rather fast. The isomers observed in such nuclei are mostly high-spin isomers
involving two-quasi-particles, four-quasi-particles and six-quasi-particles.
These isomers have all been located in 176 Hf whose decay scheme is given in
fig. 6. The 9.5 p sec. 1333.1 keV 6+ and 9.8 p sec. 1559.3 keV 8- states are
two-quasi-particle states, the 401 p sec. 14 2866 keV state is a four-quasi-
particle state, and the 43 p sec 22- 4863.6 keV state is a six-quasi-particle
state. Low spin 0+ isomers among deformed nuclei can only be shape-isomers like
the ones which have been found among the transuranic elements
	
It may be
painted out that many 0+ states have been located among the excited states of
the rare-earth nucleides by (p,t) reaction. In order for the existence of the
shape isomers in trans-rare-earth region to be confirmed, reaction gamma ray
spectroscopic studies will have to be carried out.
Among the so-called vibrational nucleides, the low-lying excited states are
usually the first 2i, the second O2, and a 4 + state as shown in rigs. 7 and 8
for even-even molybdenum and ruthenium nucleides. The location of the 0 level
changes from nucleus to nucleus. If the energy difference between the 0^ and 2+
states is not too lar$e the upper 0 2 states become long-lived. The lifetime of
such states is still longer if the 02 state happens to have a nuclear structure
very different from that of the 2+ state. Examples of such isomers are given if
fig. 9 for 70 G and 
42 
Ca.
*Nuclear Fission-Vandenbosch and 1luizenga-Academic Press (1973), pp. 59-76.
- 6 -
ERecent studies of even-even selenium isotopes show a systematic shift of
the 0+ state as one goes from 76 Soto 72 So as shown in fig. 10. The 0^ state
in 72So at 937 keV is only 75 keV above the 2^ state at 862 keV and is excited
in nuclear reactions and also in the radioactive decay of 1.3 min 
72 
Dr. Similar
states occur in 74 Se. The 02
 state is excited in heavy-ion nuclear reactions And
in Clio radioactive decay of 25 min. 74 Br.
Low-lying 0Z
 states have recently been :found in heavy ion nuclear reactions
and in the radioactive decay in light isotopes of mercury (fig. 11). In the
decay of 28-sec. 186T1 and 4.5 sec. 186m TI, the second 02 has been located at 522
keV, only 117 keV above the first 2+ state in 186 HS. In 188 HSthe second 0
state has been found at 824 kev, 57 keV below the second 2+ state. The state is
fed by the decay of 71 sec. 1$8T.1. The lifetimes have not been measured. Such
states have been theoretically predicted by Kolb and Wong in very light even-even
mercury isotopes.
'these examples illustrate the possibility that further research may reveal
an excited a isomer of suitable lifetime and energyto be suitable for gamma-ray
lasers.
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Nuclear isomer suitable for gamma ray laser

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