Documentation update

Added 2024 Paulsen article on Tc 99 measurements

docs/refs/2024_Paulsen_T99_beta_spectrum/summary.md

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+# Summary: High Precision Measurement of the ⁹⁹Tc β Spectrum
+
+## Bibliographic Information
+
+| Field | Value |
+|---|---|
+| **Title** | High precision measurement of the ⁹⁹Tc β spectrum |
+| **Journal** | Physical Review C **110**, 055503 (2024) |
+| **DOI** | 10.1103/PhysRevC.110.055503 |
+| **Received** | 5 October 2023 → Revised 16 August 2024 → Accepted 22 October 2024 → Published 20 November 2024 |
+| **Authors & Affiliations** | M. Paulsen (PTB Berlin), P. C.-O. Ranitzsch, K. Kossert, L. Bockhorn, O. Nähle (PTB Braunschweig); M. Loidl, M. Rodrigues, X. Mougeot†, A. Singh (LNHB/LNE-CEA, Paris-Saclay); J. Beyer, C. Enss (KIP Heidelberg); S. Leblond (LNHB); S. Kempf, M. Wegner, L. Bockhorn‡ (KIT) |
+| **HAL ID** | cea-04796921 |
+
+---
+
+## 1. Objective & Motivation
+
+The paper reports highly precise measurements of the **⁹⁹Tc beta decay spectrum** using **Metallic Magnetic Calorimeters (MMCs)** in two independent laboratories (LNHB, France and PTB, Germany). The goals are:
+
+- Measure the β spectrum shape down to energies < 1 keV — far below previous experiments (>50 keV threshold)
+- Extract the Q-value (maximum β energy) with unprecedented precision
+- Determine the effective axial-vector coupling constant *g*ₐ via the **spectrum-shape method**
+- Derive the average β energy, log *f*, and log *ft* for nuclear reactor modeling
+
+⁹⁹Tc is a second forbidden nonunique transition (β⁻, 99.99855%) decaying to the ⁹⁹Ru ground state. Its spectrum shape was theoretically predicted (Kostensalo & Suhonen, PR C **96**, 024317 (2017)) to be highly sensitive to *g*ₐᵉᶠᶠ, making it an ideal test case.
+
+---
+
+## 2. Decay Scheme (Fig. 1)
+
+⁹⁹Tc → ⁹⁹Ru + e⁻ + ν̄ₑ with:
+- Pure β emission [β⁻, 99.99855(30)%] to the ⁹⁹Ru ground state (reference [11])
+- Q-value previously accepted as 297.5(9) keV (AME2020, reference [17])
+
+---
+
+## 3. Experimental Methods & Setups
+
+### 3.1 Metallic Magnetic Calorimeters (MMC) — Principle
+
+MMCs are cryogenic microcalorimeters where:
+- A metallic absorber is in thermal contact with a paramagnetic sensor (Ag:Er, 300 ppm)
+- Energy deposition → temperature rise ΔT → magnetization change ΔM via:
+
+**Eq. (1):**  
+Δ*M* = (∂*M*/∂*T*) · Δ*T* = (*E* / ∂*T*) · (∂*M*/∂*T*) · (Δ*T*/*C*_tot)
+
+The magnetization change is picked up by a superconducting coil and measured with a SQUID.
+
+### 3.2 Setup Comparison: LNHB vs PTB
+
+| Parameter | **LNHB** [10,20,21] | **PTB** [28,29] |
+|---|---|---|
+| Cryostat | ¾³He dilution insert in ⁴He(l) bath | ¾³He dilution refrigerator with two-stage pulse tube precooling |
+| MMC chip | MetroBeta V1-M | MetroBeta V2-M |
+| SQUID chip | Supracon VC1A | PTB X1 |
+| Input inductance | 4.5 nH | 2 nH |
+| Absorber (Au, heat capacity) | 350 pJ/K at 20 mK | 112 pJ/K at 20 mK |
+| Sample prep | **Electrodeposited** on Au foil → diffusion welded into absorber | **Drop deposited** from NH₄⁹⁹TcO₄ solution onto Au substrate |
+| Calibration source | ¹³³Ba (~50 kBq) | ⁵⁷Co (~37 kBq) |
+| Analysis code | Optimal filtering in **MATLAB** | Optimal filtering in **PYTHON** |
+
+#### LNHB Details:
+- Operating temperature: *T* = 12 mK
+- Data acquisition: continuous stream over 13.7 days at 100 kS/s
+- Final spectrum: **7,264,451 events**, energy resolution ΔE ≈ 100 eV (constant up to 384 keV)
+
+#### PTB Details:
+- Operating temperature: *T* = 14.5 mK  
+- Data acquisition: ~20 days at 200 kS/s
+- Final spectrum: **5,326,682 counts** (after cuts)
+- Second pixel used for background measurement
+
+### 3.3 Silicon Detector Setup — PIPS at LNHB
+
+Independent confirmation using two passivated implanted planar silicon (PIPS) detectors in a quasi-4π configuration:
+- Source placed between facing detectors → >98% solid angle coverage
+- Ultrahigh vacuum, cooled to 100 K with liquid nitrogen
+- Activity ~800 Bq, dead-time <0.5%
+- Energy resolution: **9 keV at 65.52 keV** (two orders of magnitude worse than MMCs)
+- Detection threshold: ~10 keV (above MMC's sub-keV threshold)
+
+---
+
+## 4. Calibration & Linearity Correction
+
+### 4.1 Energy Calibration Lines (Table III — key entries)
+
+**LNHB (¹³³Ba source):**
+| Origin | Tabulated (keV) | Measured (keV) | ΔE (keV) | Type |
+|---|---|---|---|---|
+| ¹³³Ba Cs Kα₂ | 30.63 | 30.61 | −0.02 | X-ray |
+| ¹³³Ba Cs Kα₁ | 30.97 | 30.97 | 0.00 | X-ray |
+| Pb fluorescence (Kα₂) | 72.81 | 72.82 | +0.02 | X-ray |
+| Pb fluorescence (Kα₁) | 74.97 | 74.98 | +0.01 | X-ray |
+| Escape lines (356 keV γ − Au Kα₂) | 289.02 | 289.08 | +0.06 | Escape |
+| ¹³³Ba γ (direct) | 383.85 | 383.82 | −0.03 | Gamma |
+
+**PTB (⁵⁷Co source):**
+| Origin | Tabulated (keV) | Measured (keV) | ΔE (keV) | Type |
+|---|---|---|---|---|
+| ⁵⁷Co γ | 14.42 | 14.44 | −0.02 | Gamma |
+| Au Kα₁ fluorescence | 68.80 | 68.95 | −0.15 | X-ray |
+| Pb Kβ₁ fluorescence | 84.94 | 85.09 | −0.15 | X-ray |
+| Escape lines (122 keV γ) | ~53–55 | ±0.17 shift | — | Escape |
+
+### 4.2 Polynomial Calibration Coefficients (Table II)
+
+The energy scale was corrected for nonlinearities using a second-order polynomial:
+
+**Eq. (2):**  
+*E*_lit = *f_fit*(aᵢ) := k₁ · aᵢ + k₂ · aᵢ²
+
+| | **LNHB (Set 3)** | **PTB (Set 2)** |
+|---|---|---|
+| Linear coefficient k₁ (keV) | 355.822 | 121.355 |
+| Quadratic coefficient k₂ (keV) | 0.183 | 0.706 |
+| Linearity offset kγ₁ − 1 | 0.1% | 0.6% |
+
+The PTB nonlinearity is larger due to different detector design and thermalization.
+
+---
+
+## 5. Spectrum Corrections
+
+### 5.1 Background Subtraction
+- **LNHB approach:** Constant background + step functions below calibration peaks (since several peaks are near/above the β endpoint)
+- **PTB approach:** Dedicated second pixel provides direct background spectrum, convolved with Gaussian and scaled before subtraction
+
+### 5.2 Energy Loss Unfolding (Eq. 3–4)
+
+β electrons lose energy via Au x-ray fluorescence and bremsstrahlung. Correction uses discrete unfolding:
+
+**Eq. (3):** *h*_N^meas = R_N×N · *h*_N^true
+
+where the response matrix R is obtained from Monte Carlo simulations using **EGSNRC/egs_phd** [42].
+
+**Eq. (4):** *h*_N^algo ≈ (*R_sim*)⁻¹ · *h*_N^meas
+
+The unfolding shifted the maximum energy by approximately **+200 eV**. Energy losses were very small (<1%).
+
+---
+
+## 6. Cross-Validation Results (Table IV)
+
+| Set | Measurement | Analysis | Counts | FWHM | ETH |
+|---|---|---|---|---|---|
+| 1 | PTB | LNHB code | 3.67×10⁶ | 63 eV @ 136 keV | 345 eV |
+| 2 | PTB | PTB code | 5.33×10⁶ | 72 eV @ 136 keV | 750 eV |
+| 3 | LNHB | LNHB code | 7.26×10⁶ | 150 eV @ 303 keV | 1120 eV |
+| 4 | LNHB | PTB code | 5.66×10⁶ | 108 eV @ 303 keV | 1250 eV |
+
+All four spectra show excellent agreement — confirming the results are not dependent on analysis software or detector design.
+
+---
+
+## 7. Key Results: Q-Value & Coupling Constants
+
+### 7.1 Maximum β Energy / Q-value (Table V)
+
+The spectrum-shape method fit gives *E_max* for all four data sets:
+
+| Set | Measurement | Analysis | *E_max* (keV) | λ |
+|---|---|---|---|---|
+| 1 | PTB | LNHB | **295.809** | 0.615 |
+| 2 | PTB | PTB | **295.786** | 0.652 |
+| 3 | LNHB | LNHB | **295.845** | 0.651 |
+| 4 | LNHB | PTB | **295.862** | 0.659 |
+
+**Final weighted mean:**  
+***E_max* = *Q_β* = 295.82(16) keV** ← **Eq. (9)**
+
+This is **five times more precise** than the previously recommended value of 297.5(9) keV, and shifted by −1.8 keV (~2σ).
+
+### 7.2 Uncertainty Budget — Q-value (Table VI)
+
+| Component | LNHB u(eV) | PTB u(eV) |
+|---|---|---|
+| Energy calibration | 45 eV | 50 eV |
+| Background | **141 eV** (LNHB) / 69 eV (PTB) — *dominant* | |
+| Fit method | 93 eV | 89 eV |
+| Theoretical model | 75 eV | 75 eV |
+| Spectrum unfolding | 57 eV | 57 eV |
+
+### 7.3 Effective Axial-Vector Coupling Constant (Table VIII)
+
+The spectrum-shape method fits *g*ₐᵉᶠᶠ by comparing measured spectrum to shell-model predictions:
+
+**Best fit value:**  
+***g*ₐᵉᶠᶠ = 1.526(92)** — **Eq. (15)**, unquenched!
+
+After renormalizing half-life agreement:  
+***g*_V^eff* = 0.376(5) and *g*_A^eff* = 0.574(36)** ← **Eq. (16)**
+
+These quenched values are consistent with those for **first forbidden nonunique transitions**, solving a long-standing inconsistency noted by Suhonen [56].
+
+### 7.4 Derived Quantities — Eqs. (17)–(19)
+
+| Quantity | Value |
+|---|---|
+| Average β energy, ⟨*E_β*⟩ | **98.51(23) keV** ← Eq. (17) |
+| log *f* | **−0.476 60(22)** ← Eq. (18) |
+| log *ft* | **12.3478(23)** ← Eq. (19) |
+
+For comparison, the experimental shape factor from literature [15] gives: ⟨*E_β*⟩ = 95.91(5) keV — showing that old parametrizations are now obsolete.
+
+---
+
+## 8. Nuclear Shell Model Calculations
+
+### 8.1 Theoretical Framework (Section III.B)
+
+The β spectrum is described by the Behrens–Bühring formalism:
+
+**Eq. (5):**  
+*N*(*W*)d*W* = (*G*_β² / 2π³) · *F*(*Z*,*W*)·p*W*·(*W₀*−*W*)² · X(*W*)·C(*W*)·r(*Z*,*W*)
+
+Where:
+- *F*(*Z*,*W*) = Fermi function
+- *X*(*W*) = atomic screening and exchange corrections  
+- C(*W*) = shape factor (second forbidden nonunique)
+- r(*Z*,*W*) = atomic overlap correction, with B̈″ = 0.211(11) keV
+
+**Eq. (6):** r(*Z*,*W*) = 1 − [1/(*W₀*−*W*)] · ∂²B(G)/∂Z²
+
+### 8.2 NUSHELLX Calculations
+
+Three effective interactions were tested:
+1. **Gloeckner** [66] — GL valence space (p₁/₂, g₉/₂ for protons; s₁/₂, d₅/₂ for neutrons) → single transition dominates: *n*(2d₅/₂) → *p*(1g₉/₂)
+2. **Mach** [67] — wider GLEKPN valence space with blocked orbitals → small admixture from *n*(1g₇/₂) → *p*(1g₉/2)
+3. **jj45pnb** [68] — different sign for dominant OBTDs
+
+### 8.3 One-Body Transition Densities (Table VII)
+
+| Transition | OBTD | ΔEC(3) MeV | ΔEC(4)₁,₂ MeV | ΔEC(4)₂,₁ MeV |
+|---|---|---|---|---|
+| 1g₇/₂ → 1g₉/₂ | 0.00994 | 11.696 | 12.051 | 12.045 |
+| **2d₅/₂ → 1g₉/₂** | **0.47752** (dominant) | 10.560 | 10.536 | 10.537 |
+
+### 8.4 Coulomb Displacement Energy (Eq. 11–14)
+
+The relationship between relativistic and nonrelativistic vector matrix elements:
+
+**Eq. (11):** V²₂₁ᶠ ≃ −(*R*/√10)[*W₀* − (*mₙ*−*mₚ*) + ΔEC] · V²₂₀ᶠ
+
+Different estimates for ΔEC were tested:
+- **ΔEC⁽¹⁾** = 13.476 MeV (uniformly charged sphere) — least realistic
+- **ΔEC⁽²⁾** = 12.814 MeV (parent+daughter radii)
+- **ΔEC⁽³⁾** = 10.5 MeV (average Coulomb potential, leading order) ← used as reference
+- **ΔEC⁽⁴⁾** = full lepton current treatment — most accurate
+
+---
+
+## 9. Figures Summary
+
+| Figure | Description | Key Finding |
+|---|---|---|
+| **Fig. 1** | Decay scheme of ⁹⁹Tc | Pure β to ⁹⁹Ru ground state |
+| **Fig. 2** | Schematic overview of workflow | Data → evaluation → theory → extraction pipeline |
+| **Fig. 3** | LNHB MMC spectrum with calibration peaks (¹³³Ba) | Spectrum down to <1 keV, inset shows endpoint region |
+| **Fig. 4** | PTB MMC spectrum with calibration peaks (⁵⁷Co) | Similar quality, different source prep & analysis code |
+| **Fig. 5** | All four corrected spectra compared | Excellent agreement across all sets in linear and log scale |
+| **Fig. 6** | Normalized residual plots between analyses | Residuals <5% below 1.5 keV — cross-analysis validates methods |
+| **Fig. 7** | MMC + PIPS comparison (above 25 keV) | Three independent measurements agree perfectly; old literature spectrum diverges below 100 keV |
+| **Fig. 8** | Theoretical spectra vs measurement (varying ΔEC & CVC) | Spectrum mostly sensitive to low energy; CVC has minor effect |
+| **Fig. 9** | Effect of *g*ₐᵉᶠᶠ on spectrum shape | Strong sensitivity — *g*ₐᵉᶠᶠ between 1.4–1.6 gives good agreement |
+| **Fig. 10** | Best-fit theoretical curve (*g*ₐᵉᶠᶠ = 1.526) vs data | Excellent agreement down to 6 keV; residuals are Gaussian centered at zero |
+
+---
+
+## 10. Analysis Techniques & Methods Summary
+
+| Technique | Purpose | Implementation |
+|---|---|---|
+| **Optimal filtering** | Pulse height estimation from raw ADC data | MATLAB (LNHB) / PYTHON (PTB) |
+| **Second-order polynomial calibration** | Energy linearity correction across full range | Orthogonal distance regression (scipy.odr) |
+| **Background subtraction** | Remove ¹³³Ba/⁵⁷Co + environmental background | Constant + step functions (LNHB); direct pixel measurement (PTB) |
+| **Monte Carlo unfolding** | Correct for energy losses in absorber | EGSNRC response matrix inversion |
+| **Spectrum-shape fitting** | Extract *Q_β*, *g*ₐᵉᶠᶠ by comparing to theory | χ² minimization over theoretical curves |
+| **Nuclear shell model (NUSHELLX)** | Calculate OBTDs and shape factor C(*W*) | Three different effective interactions tested |
+
+---
+
+## 11. Overall Article Logic / Structure
+
+```
+Introduction → Motivation: why ⁹⁹Tc β spectrum matters
+   ↓
+Sec II — Experimental Study (3 measurements, independent setups)
+   ├─ A. MMC at LNHB & PTB + cross-analysis
+   └─ B. PIPS detector confirmation (>25 keV)
+   ↓
+Sec III — Combined Analysis
+   ├─ A. Q-value from Kurie-like fit → 295.82(16) keV
+   └─ B. Spectrum-shape method: shell model + gA extraction
+       ├─ Theoretical modeling (Behrens-Bühring formalism)
+       ├─ Nuclear structure (NUSHELLX, OBTDs)
+       ├─ Coulomb displacement energy estimates
+       └─ Effective coupling constants → quenched values
+   ↓
+Sec IV — Conclusion: Qβ confirmed, gAᵉᶠᶠ solved inconsistency, 
+         recommendations for Penning trap confirmation
+```
+
+---
+
+## 12. Conclusions & Implications
+
+1. **Q_β = 295.82(16) keV** — 5× more precise than previous value; −1.8 keV shift calls for Penning trap verification
+2. ***g*_A^eff* = 0.574(36)** (quenched) — resolves inconsistency between first and higher forbidden transitions
+3. **⟨*E_β*⟩ = 98.51(23) keV** — directly applicable to nuclear reactor decay heat calculations
+4. MMCs are established as the premier technique for low-energy β spectrometry (sub-keV threshold, ~100 eV resolution)
+5. Literature parametrizations of the ⁹⁹Tc spectrum must now be considered obsolete
+
+---
+
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+
+---
+
+## Extraction Quality Notes
+
+| Content Type | Extraction Quality | Notes |
+|---|---|---|
+| Full text | ✅ Excellent | All ~1180 lines extracted cleanly via pdftotext -layout |
+| Tables | ⚠️ Partially | pdfplumber returned mostly empty; full content recovered from layout text above each table |
+| Formulae | ✅ Good | LaTeX-style notation preserved (some Unicode artifacts like `99` superscripts) |
+| Figures | 📋 Described | 3 images extracted (page1: logo + decay scheme; page2: small icon); cannot render but captions and content described from text |
+| Bibliography | ✅ Complete | All 73 references extracted in full with DOIs/journal info |