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Nuclear Gamma-Ray Laser of Optical Range
E. V. Tkalya
Institute of Nuclear Physics, Moscow State University, Moscow, Russia May 24, 2011


L.A. Rivlin Nuclear gamma-ray laser: the evolution of the idea. Quantum Electronics 37 (N8) 723-744 (2007)
The evolution of the foreign and native search for solving the problem of a nuclear gamma-ray laser (NGL), which has been attracting attention for almost half a century despite the absence at present of any convincing data about its experimental solution, is considered. It is shown that the key conflict inherent in any conception of the NGL is the antagonism between the necessity to accumulate a sufficient amount of excited nuclei and the requirement to narrow down the emission gamma-ray line to its natural radiative width. The critical analysis of different approaches for solving this coneict (Mossbauer scheme, deeply cooled ensembles of free nuclei with the hidden inversion, nuclear inversionless ampliecation, two-quantum gamma emission in counter-propagating photon beams, hypothetical amplifying medium of long-lived isomers in a Bose e Einstein condensate) shows that this search is important not only due to the expected result, which could stimulate the development of quantum nucleonics as a new branch in physics, but also is of interest due to a variety of physical disciplines and experimental approaches used in this search.


-
(VUV) 229mTh (3/2+, 7.6 eV) - : 1) 229mTh, , ; 2) , ; 3) ( ); 4) ( ) .





Energy of the isomeric level
Phys.Rev.Lett. 98, 142501 (2007) B.R.Beck, J.A.Becker, P.Beiersdorfer et al. Lawrence Livermore National Laboratory, Los Alamos National Laboratory, NASA Goddard Space Flight Center : U-233 (105 Ci) : NASA/electron beam ion trap x-ray microcalorimeter spectrometer : 26 eV (FWHM).

Eis = 7.6 +/- 0.5 eV



... M1 : 229mTh(3/2+, 3.5+1.0 ) . 71 (2000) 449.


N

*

N

Эн

M1
Nucleus

E.V.Tkalya et al. Decay of the low-energy nuclear isomer 229mTh(3/2+, 3.5+/-1.0 eV) in solids (dielectrics and metals): A new scheme of experimental research. Phys.Rev.C 61 (2000) 064308. .., ... Зо н а п роводим ости 3.5+0.5 229Th ерг ическая щ ель 6 эВ ет . 67 (1998) 233. B(M1)Wu = 4.8 Ч10-2
Валентная зо на
229

Двуо кись то рия -

ThO2

Eis = 3.5+/-1.0 eV: 10 - 1

M1 "n": Wmedium = n3 Wvacuum


Structure and parameters of LiCaAlF6
S. Kuze et al. J. Solid State Chem. 177 (2004) 3505 S. Kuck et al. Laser Phys. 11 (2001) 116 Symmetry: Trigonal Band gap: 110 nm (11.1 eV) Melting temperature: 825њC
229

Th:LiCaAlF6 = 7.6 eV


N

*

N

T1/2 25 min if the refractive index 1/2 = 1


The amplification coefficient
2 n gr is rad 1 nis - - = g 2 tot 1 +

cm-1
= 1. 5

Eis = 7.6 + 0.5 eV

is = 163 + 11 nm
rad ( M 1; is gr ) 3Ч10
-19

g=

2 J gr + 1 2 J is + 1

eV

T1is2 25 min /

W.G. Rellergert et al. Phys.Rev.Lett. 104, 200802 (2010). The sample 232Th:LiCAF , n (232Th) = 1018 cm-3
229mTh:LiCaAlF 6

tot 7 Ч 10 eV ( = 1 kHz)
-13

=0

0.01 cm-1


229
J


Th

J



E (keV)
+

E (keV)
+

11/2

195.71

11/2

163.26

9/2 9/2
+

+

125.41

97.13

M1
7/2
+

71.82

The M1 transition 9/2+(97.13 keV)7/2+(71.82 keV): B(M1)W.u. = 0.038, 0.024, and 0.014 The Coriolis interaction between rotational bands enhances the transition probability by a factor of 1.2-1.3 The ``enhanced'' average value for the transition 3/2+(7.6 eV)5/2+(0.0): B(M1)W.u. = 0.032

7/2

+

42.44 5/2

+

29.19 0.0076

5/2

+

0.0

3/2

+

5/2[633]

3/2[631]

The value of the radiative width: rad = 3Ч10-19 eV


229

Th:LiCaAlF6

The Abundance Ratio

of the Isotopes, % Li : Ca:
6 7

Spin 1+ 3/20+ 0+ 7/20+ 0+ 0+ 5/2+ 1/2+ 5/2+ 0+

The ground state /N Q, eb +0.822 +3.2564 -0.818Ч10 -0.0406
-3

Li Li Ca Ca Ca Ca Ca Ca Al F Th Th

7.5 92.5 96.94 0.647 0.135 2.09 0.004 0.187 100 100 100

40 42 43 44 46 48

-1.31726

-0.043

Al: F: Th:

27

+3.64 +2.6289 +0.46

+0.1402

19

229 232

+4.3


Excitation of

229mTh(7.6

eV) by laser radiation
Initial Conditions
nis (0) = 0
is

dnis / dt = n gr - is nis - g n

is

dn gr / dt = - n gr + is nis + g n
2 is rad 1 = 10 2 L g

n gr (0) = 1018

cm-3

-24

cm2
Nist Ngrt

1Ч10

18

L / L = 10

-6
Nist+Ngrt

7.5Ч10

17

is = rad = ln 2 / T1is2 /

5Ч10

17

2.5Ч10

17

10

20

cm-2 s

-1
0 1Ч10
3

nis 1 n gr 3
2Ч10 t
3

3Ч10

3

4Ч10

3

t (2 - 3)T1is2 /


VUV Lasers
The energy of the isomeric level is known roughly, and we can not tell now, what VUV laser will be used for the pumping of the 229mth isomers. 1. We can use one of the available lasers
(see in Springer handbook of atomic, molecular, and optical physics. G.W.F. Drake (Ed.), Springer, 2nd ed., 2006).

2. It will be necessary to develop a special laser with the corresponding wavelength. 3. We can use a free electron laser (such lasers have a good tunability). For irradiation of the sample we need density of the photon flux 1020 cm-2 s-1. Such flux density can be reached relatively easily by focusing of the radiation of middle power laser.

Commercially available lasers have the power P = 1-3 W. Molecular CO and H2 lasers span region around 164 nm.


The Mossbauer effect in the optical range
The energy lost ER due to the recoil is negligibly small:

E R = 2 / 2 M = 1.4Ч10-10 eV
(M is the Th-229 nucleus mass, = 7.6 eV) The Debye-Waller factor

f exp(-3E R / 2 D ) = 1

because ER/ D << 1 (D is the Debye temperature) Emission of the -ray photons by the 229mTh isomers and the resonant absorption of these photons by the 229Th nuclei in a solid should occur without recoil.


Splitting in external magnetic field
Populations of the Zeeman sublevels are described by

exp(-

gr ( is )

H /T )

The magnetic moment of the ground state gr = 0.45 N The magnetic moment of the isomeric state is = -0.08 N (theoretical estimation)

N is the nuclear magneton
The population of the ground state sublevels falls down much faster, than the populationof the isomeric sublevels because

| gr / is | 6


Splitting in magnetic field H = 100 T at T = 0.01 K
229m

E, eV 7.6

J 3/2
+

Th

229

Th

m
3/2 1/2 -1/2 -3/2

n, cm

-3
16

= -0.08 B

5.3 Ч 1016 7 . 1 Ч 10 16 9.5 Ч 1016

4 . 0 Ч 10

=2.5Ч10-7 eV

M1
-5/2 -3/2

1.6 Ч1014
8.3 Ч1014

0

5/2

+

-1/2 1/2 3/2 5/2

4.3Ч1015

= +0.45 B

2.2 Ч1016
1.2 Ч1017

=1.4Ч10-6 eV

6.0 Ч1017

Population of the sublevels of the ground state and the isomeric state corresponds to the folloving case: Laser: P = 30 mW Density of Th-229: ngr(0) = 1018 cm-3

The amplification coefficient for "red" transitions 3 cm-1


Structure and parameters of LiCaAlF6
J.B. Amaral et al. J. Phys.: Condens. Matter 15 (2003) 2523


Structure of

229Th:LiCaAlF 6

R.A. Jackson et al. J. Phys.: Condens. Matter 21 (2009) 325403 Computer modelling of thorium doping in LiCaAlF6 Site Reaction Ca2+ ThF4 + CaCa ThћћCa + 2FI- +CaF2
Interstitial positions Unbound Bound

Solution energies (eV) for Th4+ doping in LiCAF


Quadrupole splitting.
Spectroscopic quadrupole moments The ground state spectroscopic quadrupole moment Qgr = 3.149+0.032 eb (4.3+0.9 eb - from the optical determinations ). We make the standard assumption that the intrinsic quadrupole moment Q2 = 8.816 eb remains the same for the rotational bands K = 5/2 and K = 3/2 in Th-229. 2 3K is - J is ( J is + 1) Q20 Qis = ( J is + 1)( 2 J is + 3) Then the isomeric state spectroscopic quadrupole moment Qis = 1.8 eb (2.4 eb).


Quadrupole splitting.
The electric field gradient (EFG)
"Wien2k": EFG at the Ca2+ ion site in LiCAF is zz = - 1.2Ч1017 V/cm2 In the 229Th:LiCaAlF6 crystal the leading contribution to EFG at the Th4+ ion site comes from F- ions, which compensate the extra charge 2+. These ions are located in interstitial sites in the vicinity of Th4+. An estimation gives zz -1018 V/cm2 at the Th4+ site.


Quadrupole splitting.
The Sternheimer antishielding factor
K.D. Sen and P.T. Narasimhan. Quadrupole antishielding factors and polarizabilities in ionic crystals. Phys.Rev.B (Solid State) 15 (1977) 95.

-120 -140

-110

Th : inf = -143

4+

Th : inf = -114 Ac
3+

4+

The Sternheimer Factor, Free Ion

The Sternheimer Factor, Crystal

-160 -180 -200 -220 -240 -260 -280 -300 0,9 1,0 1,1 1,2 1,3 1,4

Ac

3+

y = A1*exp(-x/t1) + y0 y0=-310.31962 A1=4123.5073 t1=0.30919 y(0.99) = -142.558

-120 -130 -140 -150 -160 -170 -180 -190

Th4+
Ra
2+

-100
Fr
+

Ra

2+

Fr
1,5 1,6 1,7

+

1,8

0,9

1,0

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

Ionic radius, A

Ionic radius, A


Quadrupole splitting
J 3/2
+

22 9

Th

m
+ 3/2 -

J 3/2
+

229

Th

m
+ 3/2 -

The sublevels energies are given by
E m = eQ
gr ( is )

+ 1/2 -

+ 1/2 -

(1 - )

3m 2 - J
zz

gr ( is )

(J

gr ( is )

+ 1)

R

B
+ -

R
5/2

B
+ 5/2 -

4J
-5

gr ( is )

(2 J

gr ( is )

- 1)

5/2

+

+ 3/2 + 1/2 -

5/2

+

+ 3/2 + 1/2 -

|is>

= 3.6 Ч 10
-5 -5

eV eV eV

( a)

(b )

|gr> = 4 Ч 10

The amplification coefficient (a) 2 cm-1 (b) 3 cm-1

= 2 Ч 10

At large values of EFG the effective inverse population and the amplification condition will hold up to the temperature T = 0.1 K.


Duration of the -ray laser emission,
102 s if D = 10-2 cm , L = 5 cm , = 3 cm-1

T1is2 ( L / D ) 2 exp(- L) /
<< T1is2 , L << -1 ln( N is / 2) /
The Fresnel number F = D 2 / 4 Lis F = 10 if L = 0.5 cm, F = 1 if L = 5 cm
N is = n

D
is

2

4

L 4 Ч 1013



The emission will be a sequence of pulses with the repetition frequency ln 2 2 5 4 -1 f rep = Qis ( D / L ) 10 - 10 s where Qis = is N is 2 Ч 1010 s-1 T1 / 2 The mean power of the -ray laser will be P 10-7 W. The gain: exp(L) 3Ч10
6


Nuclear spin relaxation process.
Inelastic scattering of the conduction electrons on nucleus or "internal" conversion on the conduction electrons
r
Energy of the Zeeman (or quadrupole) splitting of nuclear sublevels


E = 10-6 - 10


-7

eV eV

D<
Energy of the conduction electrons

E e = E F 5.5
pi = 2 m e E
F

p f = 2 m e ( E F + E )
= 1 q
min

The virtual photon

= E

q = p f - pi qmin = E me / 2 E

F



0.1 - 1 cm

m* = q2 - 2 qmin

t / m*

r = c t 1 / m* 0.1 - 1 cm

!



e
_

e

_

... 229Th(3.5 ) . 70 (1999) 367.

N

*

N

: ( ). . "" < 1




H

int

=e

2



d r d R f ( r ) i ( r ) g
3 3





e i|r - R| + ^ f ( R ) J i ( R ) N |r - R|

-



M1

32 2 2 4 Ee = e ln B( M 1) 9 E



E << Ee << me


Nuclear spin relaxation process
The "spin-lattice" relaxation time T1

1 E ne e D T1 EF
22

F

The conduction electron density (Au, Cu, Ag) ne (6 ч 8) Ч 10

cm-3

e ( M 1, = 0.45 N , E = 10-6 ч 10-7 eV ) 10
F = 2 E F / me 4.6 Ч 10
-3

-30

cm-2
e

D e ( D) /

D ( D = 0.01 cm ) 0.1

T1 50

d

E.Klein, Relaxation Phenomena. In: Low-Temperature Nuclear Orientation. Eds. N.J.Stone and H. Postma, (North-Holland, Amsterdam, 1986) p.579.

...In insulators without electronic moments... (i.e. in pure crystals)... at millikelvin temperatures... T1 would exceed the age of the Universe...


?
1. 10-6 a) , 5/2+(29.19 keV) ; b) . 2. 229Th:LiCAF. 2. T1 229Th:LiCAF. 3. 229Th:LiCAF. 4. . 5. '' . ..



- E.V.Tkalya et al. Decay of the low-energy nuclear isomer 229mTh(3/2+, 3.5+/-1.0 eV) in solids (dielectrics and metals): A new scheme of experimental research. Phys.Rev.C 61 (2000) 064308.
229

Th
97.13 71.78 42.44 29.19
= 0.8

9/2

+

7/2 7/2
+

+

Advanced Photon Source at ANL I = 100-300 mA, E = 7 GeV, C = 32.6 keV : 106 /c 1
229Th

5/2 5/2
+

+

3/2 5/2[633]

+

0.0035 3/2[631]


Nuclear spin relaxation process
The Fermi-Dirac distribution for electrons
1.0 0.8 0.6 0.4 0.2 1 2 3 4 5 6 7

fe (E) =

E T

1 E - EF exp +1 T


Nuclear Gyroscope
93

Nb:

I=9/2+, = 6.17 N Polarization

H = 10 T T = 0.02 K

Ei = Hmi
93

ni = e

-

Ei kT

/


i

n

i

1 f1 = I


i

mi ni = 0.894

Nb2O
10

5

- dielectric, 3.9 eV cm2 T1 1 h



-28

M1