HOW TO DRAW A LEVEL SCHEME ?or

ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA

N. NICA

TEXAS A&M UNIVERSITY

? ? ?

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)

Level Schemes

171Yb 155Er

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”

Moments of Inertia: Band ( band ) and Effective ( eff ) Collective Non-collective

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

Coincidence Matrix

Coincidence Matrix

E2

E1 E1

E2

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.

Sample of repeatability around reference band [541]1/2- of 163Tm Repeatable satellite peaks on the regular grid with dgrid = 3.2 keV

EDistribution Repeatability Non-repeatability

Proj

ectio

n

Proj

ectio

n

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

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!

Repeatability of [541]1/2- band in 163Tm DS(dist) distribution Dgrid = 0.8 keV

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)

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

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

Repeatability in 168Yb (all-bands reference)

ΔEγ distribution of type “S”

DS(dist) revealing repeatability pattern with dgrid ≈ 3.0 keV

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”

ΔEγ Differential Distributions

-10:10 keV, 0.1 keV/ch -50:50 keV, 1 keV/ch -200:200 keV, 40 keV/ch

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

Consequences on levels schemes

Comparison of Fluctuation Analysis Method (FAM)

and ΔEγ Distribution Method (2DΔEγ)

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

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