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spin-parity-notation-instructions

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UpdatedMay 11, 2026 at 01:07

Use this skill as a reference guide for ENSDF spin-parity (Jπ) notation rules. Covers L-transfer field positioning at column 56, J-π assignment confidence levels using parentheses, single/multiple/range spin assignments, and critical parentheses placement rules. Suitable for writing J-π values in L-records or J$ comment lines.

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sunlijie-msu

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name	spin-parity-notation-instructions
description	Use this skill as a reference guide for ENSDF spin-parity (Jπ) notation rules. Covers L-transfer field positioning at column 56, J-π assignment confidence levels using parentheses, single/multiple/range spin assignments, and critical parentheses placement rules. Suitable for writing J-π values in L-records or J$ comment lines.
argument-hint	["spin-parity expression or L-record line"]

ENSDF Spin-Parity Interpretation Reference

ENSDF 80-column data record and field definitions, structural rules, column positions, and uncertainty notation: .github/agents/ENSDF-Agent.agent.md. Spot-check policy: .github/copilot-instructions.md.

L-Transfer Field Positioning

L-Transfer Field Positioning Rule

L always starts from column 56 (EXACT rule for L transferred angular momentum fields)
L=1 → 1 at column 56
L=1+2 → 1 at column 56, +2 at columns 57-58
L=1,2 → 1 at column 56, ,2 at columns 57-58
ONLY the first L-value must be at column 56; subsequent values follow sequentially

L-Transfer from 0+ for J-π Assignment Rules

Physics mapping (single-nucleon transfer from a 0+ even-even target):

j = L ± 1/2
π = (−1)^L

L-Transfer values and corresponding J-π assignments:

L=0 → J-π: 1/2+
L=1 → J-π: 1/2-,3/2-
L=2 → J-π: 3/2+,5/2+
L=3 → J-π: 5/2-,7/2-
L=4 → J-π: 7/2+,9/2+

J-π Assignment Notation

Fundamental Rule

CRITICAL: J = spin; π = parity

WITHOUT parentheses: Firm, well-established assignments (e.g., 3/2+, 7/2-, 0+, 5-)
WITH parentheses: Less certain, tentative assignments (e.g., (3/2+), (7/2)-, 0(+), (5-))
Parentheses indicate uncertainty in the assignment confidence, not the measurement precision
With/without parentheses and the placement of parentheses are critical for conveying the confidence level of the assignment

Basic Single Assignments

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
`1/2-`	Firm	Firm	Impossible	Impossible	—
`(9/2+)`	Tentative	Tentative	Possible	Possible	—
`7/2(+)`	Firm	Tentative	Impossible	Possible	—
`(5/2)-`	Tentative	Firm	Possible	Impossible	—
`(11/2)`	Tentative	Unknown	Possible	Possible	—
`+`	Unknown	Firm	Possible	Impossible	—
`(+)`	Unknown	Tentative	Possible	Possible	—

Multiple Spin Assignments

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
`1/2-,3/2-`	Firm	Firm	Impossible	Impossible	1/2- or 3/2-
`(5/2+,7/2+)`	Tentative	Tentative	Possible	Possible	5/2+ or 7/2+ or low-probability other Jπ
`(7/2,9/2)-`	Tentative	Firm	Possible	Impossible	7/2- or 9/2- or low-probability other J-
`1/2,3/2(+)`	Firm	Tentative	Impossible	Possible	1/2± or 3/2+ or low-probability 3/2-
`(1/2,3/2,5/2)-`	Tentative	Firm	Possible	Impossible	1/2- or 3/2- or 5/2- or low-probability other J-
`(3/2,5/2,7/2+)`	Tentative	Mixed	Possible	Possible	3/2± or 5/2± or 7/2+ or low-probability other Jπ

Range Assignments

Range Parity Rules:

A:B+ or A:B- — parity applies ONLY to endpoint B; intermediate values have ±
(A:B)+ or (A:B)- — parity applies to ALL values A through B
A:B(+) or A:B(-) — tentative parity applies ONLY to endpoint B

Column Definitions:

Other Spin?: Whether spin values beyond those explicitly shown in the expansion are possible
Other Parity?: Whether parity values beyond those explicitly shown in the expansion are possible (note: ± notation counts as showing both parities)

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
`1/2:7/2`	Firm	Unknown	Impossible	Possible	1/2± or 3/2± or 5/2± or 7/2±
`(1/2:7/2)`	Tentative	Unknown	Possible	Possible	1/2± or 3/2± or 5/2± or 7/2± or low-probability other Jπ
`1/2+:7/2+`	Firm	Mixed	Impossible	Impossible	1/2+ or 3/2± or 5/2± or 7/2+
`1/2-:7/2+`	Firm	Mixed	Impossible	Impossible	1/2- or 3/2± or 5/2± or 7/2+
`1/2:7/2+`	Firm	Mixed	Impossible	Impossible	1/2± or 3/2± or 5/2± or 7/2+
`1/2+:7/2`	Firm	Mixed	Impossible	Impossible	1/2+ or 3/2± or 5/2± or 7/2±
`(1/2+:7/2+)`	Tentative	Mixed	Possible	Possible	1/2+ or 3/2± or 5/2± or 7/2+ or low-probability other Jπ
`1/2(+):7/2(+)`	Firm	Tentative	Impossible	Possible	1/2+ or 3/2± or 5/2± or 7/2+ or low-probability 1/2-, 7/2-
`(1/2:7/2+)`	Tentative	Mixed	Possible	Possible	1/2± or 3/2± or 5/2± or 7/2+ or low-probability other Jπ
`(1/2+:7/2)`	Tentative	Mixed	Possible	Possible	1/2+ or 3/2± or 5/2± or 7/2± or low-probability other Jπ
`1/2:7/2(+)`	Firm	Tentative	Impossible	Possible	1/2± or 3/2± or 5/2± or 7/2+ or low-probability 7/2-
`(1/2:7/2)+`	Tentative	Firm	Possible	Impossible	1/2+ or 3/2+ or 5/2+ or 7/2+ or low-probability other J+
`(1/2:7/2)(+)`	Tentative	Tentative	Possible	Possible	1/2+ or 3/2+ or 5/2+ or 7/2+ or low-probability other Jπ
`1/2(+),3/2(+),5/2(+),7/2(+)`	Firm	Tentative	Impossible	Possible	1/2+ or 3/2+ or 5/2+ or 7/2+ or low-probability other 1/2-, 3/2-, 5/2-, 7/2-

Note: The last entry is too long for the J field (cols 23-39) and should be placed in the 2 L continuation record.

Mixed Confidence Patterns

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
`1/2+,3/2-`	Firm	Firm	Impossible	Impossible	1/2+ or 3/2-
`3/2-,(5/2-)`	Mixed	Firm	Mixed	Impossible	3/2- or (5/2-)
`(7/2)+,9/2+`	Mixed	Mixed	Mixed	Mixed	(7/2)+ or 9/2+
`1/2(+),3/2-`	Firm	Mixed	Mixed	Mixed	1/2(+) or 3/2- or low-probability 1/2-
`(5/2+,7/2-)`	Tentative	Tentative	Possible	Possible	5/2+ or 7/2- or low-probability other Jπ
`3/2,5/2,7/2`	Firm	Unknown	Impossible	Possible	3/2± or 5/2± or 7/2±
`(1/2,3/2,5/2)`	Tentative	Unknown	Possible	Possible	1/2± or 3/2± or 5/2± or low-probability other Jπ

Critical Formatting Rules

Comma separation for multiple possibilities within same confidence level
Parentheses apply to the entire group when wrapping multiple values
Do not include explicit parity on an item inside a grouped tentative list; if a subset has a different parity or confidence, split it out of the group
Mixed notation is allowed by splitting: e.g., 1/2,3/2,5/2+ (first two tentative, parity unspecified; last firm positive)
No spaces around commas in J-π field
Exact reproduction required — never modify parentheses placement without experimental justification

Critical Parentheses Matching Rule

Spin-parity with/without parentheses convey different confidence levels. When creating J$ comments or adding values to J fields from reference data sources, ensure parentheses are preserved exactly as written in the source:

Source shows 3/2 → Comment: J$3/2 from [reference] (NO parentheses)
Source shows (3/2) → Comment: J$(3/2) from [reference] (single parentheses preserved)
NEVER use double parentheses: J$((3/2)) is FORBIDDEN
Examples: (1/2+), 1/2(+), 1/2+ represent different assignment confidence levels and the placement of parentheses must be matched accurately and precisely!

Additional Notation

Ranges: 1/2:7/2 expands to 1/2, 3/2, 5/2, 7/2. Lists: 3/2, 5/2 expands to set of both. Parity Inheritance: (1/2, 3/2)+ applies + parity to both inner items, i.e., (1/2)+, (3/2)+. Loose Matching: Parentheses () indicate tentative values.