how to draw a level scheme ? or about the nature of gamma-ray spectroscopy data n. nica texas...
TRANSCRIPT
![Page 1: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/1.jpg)
HOW TO DRAW A LEVEL SCHEME ?or
ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA
N. NICA
TEXAS A&M UNIVERSITY
? ? ?
![Page 2: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/2.jpg)
Concept: Data Evaluation - Rearguard of Research
• ENSDF-NDS data evaluation (sponsor: NNDC)
• Quantitative improvement of data through ICC precise measurement (sponsor: Texas A&M University)
• Qualitative reassessment of significance in γ-ray spectroscopy data (measurement & data research; sponsor: HOBBY)
![Page 3: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/3.jpg)
Level Schemes
171Yb 155Er
![Page 4: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/4.jpg)
![Page 5: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/5.jpg)
Moments of Inertia 1. Collective rotations – “I(I+1) rule” directly – generating rotational bands based on particular intrinsic configurations (band heads)
)1(2
)(2
IIIE
where is the moment of inertia of the deformed core of nuclei in between closed shells , and I is the (total) nuclear spin
iRI
R is the angular momentum of the rotating core
i is the intrinsic single-particle angular momentum 2. Non-collective rotations – of spherical nuclei at closed shells, where the nuclear spin results from successive single-particle alignments and the “I(I+1) rule” is satisfied “on average”
![Page 6: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/6.jpg)
Moments of Inertia: Band ( band ) and Effective ( eff ) Collective Non-collective
![Page 7: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/7.jpg)
Consequences of “I(I+1)” Rule
E2 γ-ray energy:
)12(2)24(2
)2()(2
IcIIEIEE
Rotational parameter:
2
2c
γ-ray energy difference
cIEIEE 82
8)2()(2
![Page 8: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/8.jpg)
Coincidence Matrix
![Page 9: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/9.jpg)
Coincidence Matrix
E2
E1 E1
E2
![Page 10: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/10.jpg)
Repeatability 1: Study of distributions of differences of γ-ray coincidence energies REPEATABILITY: - Repeated appearance of satellite peaks relative to the coincidence peaks of a reference rotational band at same location.
- The repeatability peaks are situated on a regular grid with characteristic distance dgrid:
ZnmdndmEEEE
EE
gridgridssrr
,),,(),(),(
),(
2121
21
- The repeatability peaks appears “statistically” at a number of repeatability positions, including the windows situated on the diagonal of the central valley.
![Page 11: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/11.jpg)
Sample of repeatability around reference band [541]1/2- of 163Tm Repeatable satellite peaks on the regular grid with dgrid = 3.2 keV
![Page 12: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/12.jpg)
EDistribution Repeatability Non-repeatability
Proj
ectio
n
Proj
ectio
n
![Page 13: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/13.jpg)
Distribution of distances D(dist) ofEdistribution
Repeatability Non-repeatability
Projection of
D(dist)
E distribution
543210
125
100
75
50
25
125
100
75
50
25
543210
1 2 3 40 E(keV)
1 2 3 40
1 2 3 40 (keV)E
(keV) 1 2 3 40-1-2-3-4 -1-2-3-4-1-2-3-4 (keV)
Cou
nts
Cou
nts
Cou
nts
Cou
nts
![Page 14: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/14.jpg)
Repeatability of [411]1/2+ band in 163Tm
ΔEγ from upper half of coinc. matrix (case “I”): dgrid = 4.5 keV
Distributions D(dist): dgrid = 4.5 keV IMP!: Fractal-like structure of hierarchized maxima!
![Page 15: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/15.jpg)
Repeatability of [541]1/2- band in 163Tm DS(dist) distribution Dgrid = 0.8 keV
![Page 16: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/16.jpg)
Repeatability in 163Tm (all-bands reference, “total reference”)
ΔEγ distribution (1 kev/ch) reveal large scale repeatability pattern with dgrid ≈ 2.7 keV
Detail of same ΔEγ distribution (0.1 kev/ch – default value)
![Page 17: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/17.jpg)
Repeatability in 163Tm (all-bands reference) – cont.
DR(dist) for the detail of ΔEγ (previous figure), revealing oscillations around plateau
Repeatability pattern with dgrid ≈ 2.65 keV
![Page 18: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/18.jpg)
Repeatability in 162Tm (all-bands reference)
ΔEγ distribution of type “R” (black points, superposed with their fit with 2D spline functions)
DR(dist) revealing repeatability pattern with dgrid ≈ 3.4 keV
![Page 19: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/19.jpg)
Repeatability in 168Yb (all-bands reference)
ΔEγ distribution of type “S”
DS(dist) revealing repeatability pattern with dgrid ≈ 3.0 keV
![Page 20: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/20.jpg)
Repeatability findings
Nucleus Dgrid (keV) / Ref. type Obs. 163Tm odd
2.65 (total)
4.5 ([411]1/2+)
0.8 ([541]1/2-)
2.65 = (4.5+0.8)/2
162Tm odd-odd
3.4 (total)
168Yb even-even
3.0 (total)
Repeatability: -Regular & Symmetrical Grid of repeated satellite peaks -Everywhere in the coincidence matrix including central valley -Structure of Recursively-Hierarchized Maxima “fractal-like”
![Page 21: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/21.jpg)
ΔEγ Differential Distributions
-10:10 keV, 0.1 keV/ch -50:50 keV, 1 keV/ch -200:200 keV, 40 keV/ch
![Page 22: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/22.jpg)
Repeatability is an Overabundant Property:• Affecting the bulk of data• Sampled manifold repeatability experimental coincidence data
and published data level schemes• It is not outstanding or astounding• Can not be seen in 1D gate spectra• It is dissimulated in 2D coincidence data• Observance & understanding are gradual and cumulative• It is the “tissue” rotational structures are made of• General property that can not be reduced to known phenomena• Does not contradict but include known physics
REPEATABILITY IS THE TRUE NATURE OF GAMMA-RAY SPECTROSCOPY DATA
![Page 23: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/23.jpg)
Consequences on levels schemes
![Page 24: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/24.jpg)
Comparison of Fluctuation Analysis Method (FAM)
and ΔEγ Distribution Method (2DΔEγ)
![Page 25: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/25.jpg)
FAM 2D ΔEγ
- Macroscopic-microscopic paradigm (order-random) :
- Macro = liquid drop = order = “8c” effective rotor periodic ridges distance
- Micro = quantum shell = randomness = ridges dispersion
- LS: Juxtaposition of single rotational bands
- Deformed potential - Classical-Quantum- Clumsy & non-visual sense- Data: Exclusive & Linear- Passive Data & Active Theory
- Complete recursive order paradigm (fractal-like order-order-order…):
- Regular(0) “8c” distances
- Regular(i), i=1,2,…(?) shorter distances (modulo repeatability)
- LS: Complete tissue-integrated rotational structures
- Geometry of recursive scales- Geometry <=> Relativity (?)- Beauty & restored visual sense- Data: Inclusive & Correlative- Balanced Data & Theory
GOD PLAY DICE GOD DOES NOT PLAY DICE
![Page 26: HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M UNIVERSITY ? ? ?](https://reader035.vdocuments.net/reader035/viewer/2022081504/5697bf901a28abf838c8da68/html5/thumbnails/26.jpg)
Conclusion• Repeatability is the true nature of the nuclear
spectroscopy data• Allowing a full decomposability “modulo
repeatability” of the data• Showing a general recursive inter-level (inter-
band) correlation property • Leading to a fully correlated structure of levels• Including non-contradictorily the known nuclear
rotation phenomena• And restoring a sense of visuability to the
quantum level of nuclear structure